Author: Calculator Academy Team
Last Updated: November 1, 2021
Enter any number into the calculator and the calculator will raise that number to the 10th power.
10th Power Formula
The following formula is used to calculate the 10th power of any number.
Y = X^10
- Where Y is the resulting value
- X is the numer being raised to the 10th power
10th Power Definition
Raising a number to the 10th power means multiplying that number by itself 10 times. For example, 5 to the 10th power would equal 5*5*5*5*5*5*5*5*5*5= 9765625.
How to raise a number to the 10th power?
Example problem #1:
For this first example problem, we will be raising the number 4 to the 10th power.
Using the formula above:
Y = X^10
= 4^10
= 4*4*4*4*4*4*4*4*4*4
= 1048576
Example Problem #2
In this next example, we will raise the number 2 to the 10th power.
Using the formula:
Y= X^10
= 2^10
= 1024
What is interesting to note about this result is that even though 2 is only half of 4, when it’s raised to the 10th power, the result is 1024 times less than 4 to the 10th power.
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The powers of 10 are easy to remember, because we use a base 10 number system.
For 10 n with n a positive integer, just write a " 1 " with n zeros after it. For negative powers 10 − n , write " 0 ." followed by n − 1 zeros, and then a 1 .
The powers of 10 are widely used in scientific notation , so it's a good idea to get comfortable with them.
Powers of 10 | |
10 1 = 10 | 10 1 = 1 |
10 2 = 100 | 10 -1 = 0.1 |
10 3 = 1000 | 10 -2 = 0.01 |
10 4 = 10,000 | 10 -3 = 0.001 |
10 5 = 100,000 (one hundred thousand) | 10 -4 = 0.0001 (one ten thousandth) |
10 6 = 1,000,000 (one million) | 10 -5 = 0.00001 (one hundred thousandth) |
10 7 = 10,000,000 (ten million) | 10 -6 = 0.000001 (one millionth) |
10 8 = 100,000,000 (one hundred million) | 10 -7 = 0.0000001 (one ten millionth) |
10 9 = 1,000,000,000 (one billion) | 10 -8 = 0.00000001 (one hundred millionth) |
10 10 = 10,000,000,000 (ten billion) | 10 -9 = 0.000000001 (one billionth) |
Click here for more names for really big and really small numbers .
This article is about the mathematical concept. For other uses, see Power of 10 (disambiguation). A power of 10 is any of the integer powers of the number ten; in other words, ten multiplied by itself a certain number of times (when the power is a positive integer). By definition, the number one is a power (the zeroth power) of ten. The first few non-negative powers of ten are:
In decimal notation the nth power of ten is written as '1' followed by n zeroes. It can also be written as 10n or as 1En in E notation. See order of magnitude and orders of magnitude (numbers) for named powers of ten. There are two conventions for naming positive powers of ten, beginning with 109, called the long and short scales. Where a power of ten has different names in the two conventions, the long scale name is shown in parentheses.
The positive 10 power related to a short scale name can be determined based on its Latin name-prefix using the following formula: 10[(prefix-number + 1) × 3]
Examples:
- billion = 10[(2 + 1) × 3] = 109
- octillion = 10[(8 + 1) × 3] = 1027
one | 0 | 1 | ||
ten | 1 | 10 | da (D) | deca |
hundred | 2 | 100 | h (H) | hecto |
thousand | 3 | 1,000 | k (K) | kilo |
ten thousand (myriad (Greek)) | 4 | 10,000 | ||
hundred thousand (lakh (India)) | 5 | 100,000 | ||
million | 6 | 1,000,000 | M | mega |
ten million (crore (India)) | 7 | 10,000,000 | ||
hundred million | 8 | 100,000,000 | ||
billion (milliard) | 9 | 1,000,000,000 | G | giga |
trillion (billion) | 12 | 1,000,000,000,000 | T | tera |
quadrillion (billiard) | 15 | 1,000,000,000,000,000 | P | peta |
quintillion (trillion) | 18 | 1,000,000,000,000,000,000 | E | exa |
sextillion (trilliard) | 21 | 1,000,000,000,000,000,000,000 | Z | zetta |
septillion (quadrillion) | 24 | 1,000,000,000,000,000,000,000,000 | Y | yotta |
octillion (quadrilliard) | 27 | 1,000,000,000,000,000,000,000,000,000 | ||
nonillion (quintillion) | 30 | 1,000,000,000,000,000,000,000,000,000,000 | ||
decillion (quintilliard) | 33 | 1,000,000,000,000,000,000,000,000,000,000,000 | ||
undecillion (sextillion) | 36 | 1,000,000,000,000,000,000,000,000,000,000,000,000 | ||
duodecillion (sextilliard) | 39 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
tredecillion (septillion) | 42 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
quattuordecillion (septilliard) | 45 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
quindecillion (octillion) | 48 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
sexdecillion (octilliard) | 51 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
septendecillion (nonillion) | 54 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
octodecillion (nonilliard) | 57 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
novemdecillion (decillion) | 60 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
vigintillion (decilliard) | 63 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
unvigintillion (undecillion) | 66 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
duovigintillion (undecilliard) | 69 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
trevigintillion (duodecillion) | 72 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
quattuorvigintillion (duodecilliard) | 75 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
quinvigintillion (tredecillion) | 78 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
sexvigintillion (tredecilliard) | 81 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
septenvigintillion (quattuordecillion) | 84 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
octovigintillion (quattuordecilliard) | 87 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
novemvigintillion (quindecillion) | 90 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
trigintillion (quindecilliard) | 93 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 | ||
googol | 100 | 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 |
||
centillion | 303 | 1,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 |
||
googolplex | googol | one then 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, 000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000 zeros. |
The sequence of powers of ten can also be extended to negative powers.
Similar to the positive powers, the negative power of 10 related to a short scale name can be determined based on its Latin name-prefix using the following formula: 10−[(prefix-number + 1) × 3]
Examples:
- billionth = 10−[(2 + 1) × 3] = 10−9
- quintillionth = 10−[(5 + 1) × 3] = 10−18
one | 0 | 1 | ||
tenth | −1 | 0.1 | d | deci |
hundredth | −2 | 0.01 | c | centi |
thousandth | −3 | 0.001 | m | milli |
ten-thousandth (Myriadth) | −4 | 0.000 1 | ||
hundred-thousandth (Lacth) | −5 | 0.000 01 | ||
millionth | −6 | 0.000 001 | μ | micro |
billionth | −9 | 0.000 000 001 | n | nano |
trillionth | −12 | 0.000 000 000 001 | p | pico |
quadrillionth | −15 | 0.000 000 000 000 001 | f | femto |
quintillionth | −18 | 0.000 000 000 000 000 001 | a | atto |
sextillionth | −21 | 0.000 000 000 000 000 000 001 | z | zepto |
septillionth | −24 | 0.000 000 000 000 000 000 000 001 | y | yocto |
octillionth | −27 | 0.000 000 000 000 000 000 000 000 001 | ||
nonillionth | −30 | 0.000 000 000 000 000 000 000 000 000 001 | ||
decillionth | −33 | 0.000 000 000 000 000 000 000 000 000 000 001 | ||
undecillionth | −36 | 0.000 000 000 000 000 000 000 000 000 000 000 001 | ||
duodecillionth | −39 | 0.000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
tredecillionth | −42 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
quattuordecillionth | −45 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
quindecillionth | −48 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
sexdecillionth | −51 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
septendecillionth | −54 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
octodecillionth | −57 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
novemdecillionth | −60 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
vigintillionth | −63 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
unvigintillionth | −66 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
duovigintillionth | −69 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
trevigintillionth | −72 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
quattuorvigintillionth | −75 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
quinvigintillionth | −78 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
sexvigintillionth | −81 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
septenvigintillionth | −84 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
octovigintillionth | −87 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
novemvigintillionth | −90 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
trigintillionth | −93 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
googolth | −100 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 1 | ||
centillionth | −303 | 0.000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 001 | ||
googolplexth | −googol | ten to the negative 10,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,
000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000. |
Main article: Googol
The number googol is 10100. The term was coined by 9-year-old Milton Sirotta, nephew of American mathematician Edward Kasner. It was popularized in Kasner's 1940 book Mathematics and the Imagination, where it was used to compare and illustrate very large numbers. Googolplex, a much larger power of ten (10 to the googol power, or 1010100), was also introduced in that book. (Read below)
Main article: Googolplex
The number googolplex is 10googol, or 1010,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000, and was also made by Edward Kasner's nephew. (Read above)
Main article: Scientific notation
Scientific notation is a way of writing numbers of very large and very small sizes compactly when precision is less important.
A number written in scientific notation has a significand (sometime called a mantissa) multiplied by a power of ten.
Sometimes written in the form:
m × 10nOr more compactly as:
10nThis is generally used to denote powers of 10. Where n is positive, this indicates the number of zeros after the number, and where the n is negative, this indicates the number of decimal places before the number.
As an example:
105 = 100,000[1] 10−5 = 0.00001[2]The notation of mEn, known as E notation, is used in computer programming, spreadsheets and databases, but is not used in scientific papers.
- Power of two
- Power of three
- SI prefix
- Cosmic View, inspiration for the film Powers of Ten
- Exponentiation
- Powers of Ten (1977). Nine-minute film. US Public Broadcasting Service (PBS), made by Charles and Ray Eames. "An adventure in magnitudes. Starting at a picnic by the lakeside in Chicago, this film transports the viewer to the outer edges of the universe. Every ten seconds we view the starting point from ten times farther out until our own galaxy is visible only as a speck of light among many others. Returning to Earth with breathtaking speed, we move inward - into the hand of the sleeping picnicker - with ten times more magnification every ten seconds. Our journey ends inside a proton of a carbon atom within a DNA molecule in a white blood cell."
- ^ "Powers of 10". www.mathsteacher.com.au. Retrieved 2020-03-17.
- ^ "Powers of Ten". hesperia.gsfc.nasa.gov. Retrieved 2020-03-17.
Retrieved from "//en.wikipedia.org/w/index.php?title=Power_of_10&oldid=1105756602"
Page 2
"1,000" and "Thousand" redirect here. For other uses, see 1000 (disambiguation). 1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it can be written with or without a comma or sometimes a period separating the thousands digit: 1,000.
List of numbers — Integers ← 0 1k 2k 3k 4k 5k 6k 7k 8k 9k →
← 999
1000
1001 →
(one thousandth)Factorization23 × 53Divisors1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, 1000Greek numeral,Α´Roman numeralMUnicode symbol(s)ↀGreek prefixchiliaLatin prefixmilliBinary11111010002Ternary11010013Senary43446Octal17508Duodecimal6B412Hexadecimal3E816Tamil௲Chinese千Punjabi੧੦੦੦
Look up thousand or 1000 in Wiktionary, the free dictionary.
It may also be described as the short thousand in historical discussion of medieval contexts where it might be confused with the Germanic concept of the "long thousand" (1200).
A period of 1,000 years is sometimes termed, after the Greek root, a chiliad. A chiliad of other objects means 1,000 of them.[1]
- The decimal representation for one thousand is
- 1000—a one followed by three zeros, in the general notation ;
- 1 × 103—in engineering notation, which for this number coincides with :
- 1 × 103 exactly—in scientific normalized exponential notation ;
- 1 E+3 exactly—in scientific E notation.
- The SI prefix for a thousand units is "kilo-", abbreviated to "k"—for instance, a kilometre or "km" is a thousand metres.
- In the SI writing style, a non-breaking space can be used as a thousands separator, i.e., to separate the digits of a number at every power of 1000.
- Multiples of thousands are occasionally represented by replacing their last three zeros with the letter "K": for instance, writing "$30K" for $30 000, or denoting the Y2K computer bug of the year 2000.
- A thousand units of currency, especially dollars or pounds, are colloquially called a grand. In the United States of America this is sometimes abbreviated with a "G" suffix.
- The factors of 1000 are: 1, 2, 4, 5, 8, 10, 20, 25, 40, 50, 100, 125, 200, 250, 500, and 1000.[2]
- 1000 is a Harshad number in base 10.
- The sum of Euler's totient function over the first 57 integers is 1000.
- Prime Curios! mentions that 1000 is the smallest number that generates three primes in the fastest way possible by concatenation of decremented numbers (1 000 999, 1 000 999 998 997, and 1 000 999 998 997 996 995 994 993 are prime). The criterion excludes counting the number itself.[3]
There are 135 prime numbers between 1000 and 2000:[432][433]
1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1201, 1213, 1217, 1223, 1229, 1231, 1237, 1249, 1259, 1277, 1279, 1283, 1289, 1291, 1297, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1409, 1423, 1427, 1429, 1433, 1439, 1447, 1451, 1453, 1459, 1471, 1481, 1483, 1487, 1489, 1493, 1499, 1511, 1523, 1531, 1543, 1549, 1553, 1559, 1567, 1571, 1579, 1583, 1597, 1601, 1607, 1609, 1613, 1619, 1621, 1627, 1637, 1657, 1663, 1667, 1669, 1693, 1697, 1699, 1709, 1721, 1723, 1733, 1741, 1747, 1753, 1759, 1777, 1783, 1787, 1789, 1801, 1811, 1823, 1831, 1847, 1861, 1867, 1871, 1873, 1877, 1879, 1889, 1901, 1907, 1913, 1931, 1933, 1949, 1951, 1973, 1979, 1987, 1993, 1997, 1999
Wikimedia Commons has media related to 1000 (number).
- Mathematics portal
- ^ "chiliad". Merriam-Webster. Archived from the original on March 25, 2022.
- ^ "Factors of 1000". Gcf & Lwcm. Archived from the original on 2020-11-05. Retrieved October 25, 2020.
- ^ "1000". Prime Curious!. Archived from the original on March 25, 2022.
- ^ "Sloane's A122189 : Heptanacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on October 7, 2016. Retrieved July 13, 2017.
- ^ Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
- ^ a b "A003352 - Oeis".
- ^ "A003353 - Oeis".
- ^ Sloane, N. J. A. (ed.). "Sequence A034262". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A020473". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
- ^ "A046092 - Oeis".
- ^ a b c d e f g h i j k l m n o "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 11, 2015. Retrieved June 12, 2016.
- ^ a b c d e f g h i j "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 11, 2015. Retrieved June 12, 2016.
- ^ Sloane, N. J. A. (ed.). "Sequence A000325". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
- ^ a b c d "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
- ^ a b c d e f g h "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on May 17, 2016. Retrieved June 12, 2016.
- ^ "A316729 - Oeis".
- ^ Sloane, N. J. A. (ed.). "Sequence A006313 (Numbers n such that n^16 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-05-24.
- ^ a b c d e f g h i j k l "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A332835 (Number of compositions of n whose run-lengths are either weakly increasing or weakly decreasing)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A007053". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
- ^ Richard Kenneth Guy (June 29, 2013). "A. Prime numbers". Unsolved Problems in Number Theory. Springer Science+Business Media. p. 7. ISBN 978-1475717389. Archived from the original on March 25, 2022.
- ^ "A004801 - Oeis".
- ^ a b c d e f g h "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on April 5, 2016. Retrieved June 12, 2016.
- ^ a b c d e f g h i "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on April 17, 2016. Retrieved June 12, 2016.
- ^ a b "A000124 - Oeis".
- ^ "A161328 - Oeis".
- ^ "A023036 - Oeis".
- ^ "A007522 - Oeis".
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A002865 (Number of partitions of n that do not contain 1 as a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
- ^ a b "A000695 - Oeis".
- ^ "A003356 - Oeis".
- ^ a b "A003357 - Oeis".
- ^ "A036301 - Oeis".
- ^ "A000567 - Oeis".
- ^ "A000025 - Oeis".
- ^ "A336130 - Oeis".
- ^ "A073576 - Oeis".
- ^ a b c d e f g "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
- ^ "Base converter | number conversion".
- ^ Sloane, N. J. A. (ed.). "Sequence A015723 (Number of parts in all partitions of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
- ^ "A003365 - Oeis".
- ^ "A045943 - Oeis".
- ^ "A005448 - Oeis".
- ^ "A003368 - Oeis".
- ^ a b c d e f g h i j k l m "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 9, 2016. Retrieved June 12, 2016.
- ^ "A002061 - Oeis".
- ^ "A003349 - Oeis".
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A001105". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A003294 - Oeis".
- ^ a b c "A035137 - Oeis".
- ^ "A347565: Primes p such that A241014(A000720(p)) is +1 or -1". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on March 25, 2022. Retrieved January 19, 2022.
- ^ "A003325 - Oeis".
- ^ "A195162 - Oeis".
- ^ "A006532 - Oeis".
- ^ "A341450 - Oeis".
- ^ Sloane, N. J. A. (ed.). "Sequence A006128 (Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "A006567 - Oeis".
- ^ a b "A003354 - Oeis".
- ^ a b c d e f g h "Sloane's A000566 : Heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 11, 2016. Retrieved June 12, 2016.
- ^ a b c d e f g "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 9, 2016. Retrieved June 12, 2016.
- ^ "A273873 - Oeis".
- ^ "A292457 - Oeis".
- ^ "A073592 - Oeis".
- ^ a b c d e f g h i j "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
- ^ a b c "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 10, 2016. Retrieved June 12, 2016.
- ^ "A077043 - Oeis".
- ^ "A056107 - Oeis".
- ^ "A025147 - Oeis".
- ^ "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 9, 2016. Retrieved June 12, 2016.
- ^ "Sloane's A031157 : Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on March 4, 2016. Retrieved June 12, 2016.
- ^ "A033996 - Oeis".
- ^ "A018900 - Oeis".
- ^ "A046308 - Oeis".
- ^ "Sloane's A001232 : Numbers n such that 9*n = (n written backwards)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on October 17, 2015. Retrieved June 14, 2016.
- ^ "A003350 - Oeis".
- ^ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 163
- ^ a b c d e "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Archived from the original on June 11, 2016. Retrieved June 12, 2016.
- ^ "A003355 - Oeis".
- ^ "A051682 - Oeis".
- ^ Sloane, N. J. A. (ed.). "Sequence A323657 (Number of strict solid partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "A121029 - Oeis".
- ^ "A292449 - Oeis".
- ^ Sloane, N. J. A. (ed.). "Sequence A087188 (number of partitions of n into distinct squarefree parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A059993". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ a b "Sloane's A007629 : Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ "Sloane's A002997 : Carmichael numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ a b c d e "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A001567 (Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A051890 (2*(n^2 - n + 1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A319560 (Number of non-isomorphic strict T_0 multiset partitions of weight n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A028916 (Friedlander-Iwaniec primes: Primes of form a^2 + b^4)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A057732 (Numbers k such that 2^k + 3 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A128455 (Numbers k such that 9^k - 2 is a prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000009 (Expansion of Product_{m > 0} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A318949 (Number of ways to write n as an orderless product of orderless sums)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A038499 (Number of partitions of n into a prime number of parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006748 (Number of diagonally symmetric polyominoes with n cells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A210000 (Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
- ^ Sloane, N. J. A. (ed.). "Sequence A033995 (Number of bipartite graphs with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i j Sloane, N. J. A. (ed.). "Sequence A045943". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A080040". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A264237 (Sum of values of vertices at level n of the hyperbolic Pascal pyramid)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006315 (Numbers n such that n^32 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "Sloane's A000101 : Increasing gaps between primes (upper end)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-07-10.
- ^ a b "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ a b c d "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c "Sloane's A005900 : Octahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ "Sloane's A069125 : a(n) = (11*n^2 - 11*n + 2)/2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A001845 (Centered octahedral numbers (crystal ball sequence for cubic lattice))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2022-06-02.
- ^ Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007491 (Smallest prime > n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
- ^ Sloane, N. J. A. (ed.). "Sequence A051424 (Number of partitions of n into pairwise relatively prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006748 (Number of diagonally symmetric polyominoes with n cells)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A059993". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ >Sloane, N. J. A. (ed.). "Sequence A080663 (3*n^2 - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Meehan, Eileen R., Why TV is not our fault: television programming, viewers, and who's really in control Lanham, MD: Rowman & Littlefield, 2005
- ^ Sloane, N. J. A. (ed.). "Sequence A240574 (Number of partitions of n such that the number of odd parts is a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Higgins, ibid.
- ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006355 (Number of binary vectors of length n containing no singletons)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A001110 : Square triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ a b c d e "Sloane's A016754 : Odd squares: a(n) = (2n+1)^2. Also centered octagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A008302". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A015723 (Number of parts in all partitions of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A126796 (Number of complete partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A033819 : Trimorphic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A058331 (2*n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A144300 (Number of partitions of n minus number of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A318949 (Number of ways to write n as an orderless product of orderless sums)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) is the number of partitions of n (the partition numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ a b c d e "Sloane's A014575 : Vampire numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A000009 (Expansion of Product_{m > 0} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A023894 (Number of partitions of n into prime power parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000930 (Narayana's cows sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001792". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A051424 (Number of partitions of n into pairwise relatively prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006958 (Number of parallelogram polyominoes with n cells (also called staircase polyominoes, although that term is overused))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A033548 (Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Constitutional Court allows 'FCK CPS' sticker". The Local. 28 April 2015. "...state court in Karlsruhe ruled that a banner ... that read 'ACAB' – an abbreviation of 'all cops are bastards' ... a punishable insult. ... A court in Frankfurt ... the numbers '1312' constituted an insult ... the numerals stand for the letters ACAB's position in the alphabet.
- ^ Sloane, N. J. A. (ed.). "Sequence A304716 (Number of integer partitions of n whose distinct parts are connected)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ >Sloane, N. J. A. (ed.). "Sequence A080663 (3*n^2 - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A101624 (Stern-Jacobsthal number)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A038499 (Number of partitions of n into a prime number of parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A058331 (2*n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A033548 (Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "Sloane's A000332 : Binomial coefficient binomial(n,4) = n*(n-1)*(n-2)*(n-3)/24". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A210000 (Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
- ^ Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005945 (Number of n-step mappings with 4 inputs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002414 (Octagonal pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A001567 : Fermat pseudoprimes to base 2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ "Sloane's A050217 : Super-Poulet numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A304716 (Number of integer partitions of n whose distinct parts are connected)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007865 (Number of sum-free subsets of {1, ..., n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
- ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000682 : Semimeanders". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A008302". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "Sloane's A051015 : Zeisel numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A000009 (Expansion of Product_{m > 0} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A033548 (Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003037 (Smallest number of complexity n: smallest number requiring n 1's to build using +, * and ^)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A015723 (Number of parts in all partitions of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A011379 (n^2*(n+1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A023894 (Number of partitions of n into prime power parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006128 (Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A307958 (Coreful perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000219 (Number of planar partitions (or plane partitions) of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006330 (Number of corners, or planar partitions of n with only one row and one column)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A323657 (Number of strict solid partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A034296 (Number of flat partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002071 (Number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most the n-th prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000702 (number of conjugacy classes in the alternating group A_n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). functions of exactly n variables "Sequence A000615Threshold functions of exactly n variables". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. {{cite web}}: Check |url= value (help)
- ^ Sloane, N. J. A. (ed.). "Sequence A005897". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A319066 (Number of partitions of integer partitions of n where all parts have the same length)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A307958 (Coreful perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000014 (Number of series-reduced trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A144300 (Number of partitions of n minus number of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A052486". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A058331 (2*n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A033548 (Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A005231 : Odd abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) is the number of partitions of n (the partition numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ >Sloane, N. J. A. (ed.). "Sequence A080663 (3*n^2 - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A210000 (Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
- ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A064174 (Number of partitions of n with nonnegative rank)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007584 (9-gonal (or enneagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000009 (Expansion of Product_{m > 0} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A038499 (Number of partitions of n into a prime number of parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A051424 (Number of partitions of n into pairwise relatively prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006315 (Numbers n such that n^32 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A015723 (Number of parts in all partitions of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A307958 (Coreful perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007491 (Smallest prime > n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A210000 (Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
- ^ "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A054735 (Sums of twin prime pairs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A007850 : Giuga numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ >Sloane, N. J. A. (ed.). "Sequence A080663 (3*n^2 - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005897". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007491 (Smallest prime > n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A051424 (Number of partitions of n into pairwise relatively prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A240574 (Number of partitions of n such that the number of odd parts is a part)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A054377 : Primary pseudoperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Kellner, Bernard C.; 'The equation denom(Bn) = n has only one solution'
- ^ Sloane, N. J. A. (ed.). "Sequence A006318 (Large Schröder numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-05-22.
- ^ "Sloane's A000058 : Sylvester's sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006315 (Numbers n such that n^32 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000009 (Expansion of Product_{m > 0} (1 + x^m); number of partitions of n into distinct parts; number of partitions of n into odd parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006315 (Numbers n such that n^32 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A304716 (Number of integer partitions of n whose distinct parts are connected)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007585 (10-gonal (or decagonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A210000 (Number of unimodular 2 X 2 matrices having all terms in {0,1,...,n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
- ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003037 (Smallest number of complexity n: smallest number requiring n 1's to build using +, * and ^)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A164652 (Hultman numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007530 (Prime quadruples: numbers k such that k, k+2, k+6, k+8 are all prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A011379 (n^2*(n+1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000930 (Narayana's cows sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ >Sloane, N. J. A. (ed.). "Sequence A080663 (3*n^2 - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A057568 (Number of partitions of n where n divides the product of the parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006315 (Numbers n such that n^32 + 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A011757 (prime(n^2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A004799 (Self convolution of Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005920 (Tricapped prism numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000609 (Number of threshold functions of n or fewer variables)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000702 (number of conjugacy classes in the alternating group A_n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001770 (Numbers k such that 5*2^k - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A259793 (Number of partitions of n^4 into fourth powers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A140091 (3*n*(n + 3)/2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A071395 (Primitive abundant numbers (abundant numbers all of whose proper divisors are deficient numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002061 (Central polygonal numbers: n^2 - n + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A101624 (Stern-Jacobsthal number)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006785 (Number of triangle-free graphs on n vertices)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002998 (Smallest multiple of n whose digits sum to n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A144391 (3*n^2 + n - 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005987 (Number of symmetric plane partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A023431 (Generalized Catalan Numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A034296 (Number of flat partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001567 (Fermat pseudoprimes to base 2, also called Sarrus numbers or Poulet numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A217135 (Numbers n such that 3^n - 8 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A307958 (Coreful perfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A034897 : Hyperperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A240736 (Number of compositions of n having exactly one fixed point)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002413 (Heptagonal (or 7-gonal) pyramidal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007070 (4*a(n-1) - 2*a(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A033548 (Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000412 (Number of bipartite partitions of n white objects and 3 black ones)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A027851 (Number of nonisomorphic semigroups of order n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A053767 (Sum of first n composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A051424 (Number of partitions of n into pairwise relatively prime parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003060 (Smallest number with reciprocal of period length n in decimal (base 10))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A008514 (4-dimensional centered cube numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001105 (2*n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A058331 (2*n^2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005893 (Number of points on surface of tetrahedron; coordination sequence for sodalite net (equals 2*n^2+2 for n > 0))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A318949 (Number of ways to write n as an orderless product of orderless sums)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A024012 (2^n - n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002845 (Number of distinct values taken by 2^2^...^2 (with n 2's and parentheses inserted in all possible ways))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A304716 (Number of integer partitions of n whose distinct parts are connected)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002071 (Number of pairs of consecutive integers x, x+1 such that all prime factors of both x and x+1 are at most the n-th prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A023894 (Number of partitions of n into prime power parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A033548 (Honaker primes: primes P(k) such that sum of digits of P(k) equals sum of digits of k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence n*(n+2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Sloane's A051870 : 18-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
- ^ Sloane, N. J. A. (ed.). "Sequence A045648 (Number of chiral n-ominoes in (n-1)-space, one cell labeled)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005899 (Number of points on surface of octahedron)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A208155 (7-Knödel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A008302". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000127 (Maximal number of regions obtained by joining n points around a circle by straight lines. Also number of regions in 4-space formed by n-1 hyperplanes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A178084 (Numbers k for which 10k + 1, 10k + 3, 10k + 7, 10k + 9 and 10k + 13 are primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007419 (Largest number not the sum of distinct n-th-order polygonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A052486". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A100953 (Number of partitions of n into relatively prime parts such that multiplicities of parts are also relatively prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005897". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A226366 (Numbers k such that 5*2^k + 1 is a prime factor of a Fermat number 2^(2^m) + 1 for some m)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A323657 (Number of strict solid partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007491 (Smallest prime > n^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A319014 (1*2*3 + 4*5*6 + 7*8*9 + 10*11*12 + 13*14*15 + 16*17*18 + ... + (up to n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007419 (Largest number not the sum of distinct n-th-order polygonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A055621 (Number of covers of an unlabeled n-set)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007865 (Number of sum-free subsets of {1, ..., n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.}
- ^ Sloane, N. J. A. (ed.). "Sequence A144300 (Number of partitions of n minus number of divisors of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000522 (Total number of ordered k-tuples of distinct elements from an n-element set)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000041 (a(n) is the number of partitions of n (the partition numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A104621 (Heptanacci-Lucas numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A015723 (Number of parts in all partitions of n into distinct parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000328". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005449 (Second pentagonal numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002982 (Numbers n such that n! - 1 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A030238 (Backwards shallow diagonal sums of Catalan triangle A009766)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006128 (Total number of parts in all partitions of n. Also, sum of largest parts of all partitions of n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A089046 (Least edge-length of a square dissectable into at least n squares in the Mrs. Perkins's quilt problem)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A065900 (Numbers n such that sigma(n) equals sigma(n-1) + sigma(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Jon Froemke & Jerrold W. Grossman (Feb 1993). "A Mod-n Ackermann Function, or What's So Special About 1969?". The American Mathematical Monthly. Mathematical Association of America. 100 (2): 180–183. doi:10.2307/2323780. JSTOR 2323780.
- ^ Sloane, N. J. A. (ed.). "Sequence A052542 (2*a(n-1) + a(n-2))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A024069 (6^n - n^7)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A217076 (Numbers n such that (n^37-1)/(n-1) is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006355 (Number of binary vectors of length n containing no singletons)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A064174 (Number of partitions of n with nonnegative rank)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000567 (Octagonal numbers: n*(3*n-2). Also called star numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A302545 (Number of non-isomorphic multiset partitions of weight n with no singletons)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A277288 (Positive integers n such that n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A028387 (n + (n+1)^2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A059993 (Pinwheel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A014206 (n^2 + n + 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A001608 (Perrin sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A318949 (Number of ways to write n as an orderless product of orderless sums)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005945 (Number of n-step mappings with 4 inputs)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A187220 (Gullwing sequence)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A046351 (Palindromic composite numbers with only palindromic prime factors)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000612 (Number of P-equivalence classes of switching functions of n or fewer variables, divided by 2)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ OEIS: A059801
- ^ Sloane, N. J. A. (ed.). "Sequence A038499 (Number of partitions of n into a prime number of parts)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002470 (Glaisher's function W(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A263341 (Triangle read by rows: T(n,k) is the number of unlabeled graphs on n vertices with independence number k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A089085 (Numbers k such that (k! + 3)/3 is prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A011755". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005448 (Centered triangular numbers: 3n(n-1)/2 + 1)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A038823 (Number of primes between n*1000 and (n+1)*1000)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Stein, William A. (10 February 2017). "The Riemann Hypothesis and The Birch and Swinnerton-Dyer Conjecture". wstein.org. Retrieved 6 February 2021.
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