1000 (number)

1000 or one thousand is the natural number following 999 and preceding 1001. In most English-speaking countries, it is often written with a comma separating the thousands unit: 1,000.

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).

In mathematics

The decimal representation for one thousand is
- 1,000—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 is kilo-, with the official symbol k—for instance, prefixed to "metre" or its symbol "m", kilometre or km signifies a thousand metres. As such, people occasionally represent the number in a non-standard notation by replacing the last three zeros of the general numeral with "K": for instance, 30K for 30,000.
By the SI writing style, a space can be used as a thousands separator, i.e., to separate the digits of a number at every power of 1000.
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 (1000999, 1000999998997, and 1000999998997996995994993 are prime). The criterion excludes counting the number itself.
1000 is a Harshad number in base 10.

In time

A millennium is 1000 years. The year 1000 was the last year of the 1st millennium.

In popular culture

A grand is a slang term for one thousand units of a given currency, usually dollars or pounds. Several grand can be shortened to Gs.
The symbol K is sometimes used for a thousand; for example, in referring to units of salary or in reference to the Y2K computer bug.
Especially in the United States, the gambling community often refers to denominations of $1000 as dimes.
The idiom "a picture is worth a thousand words".
According to an ancient Japanese legend, anyone who folds a thousand origami cranes will be granted a wish by a crane.
The thousandth of something is often celebrated, as with other round numbers. A good example is a millennium.

Miscellaneous

Thousand Oaks, California
Metal Mining SIC Code
Thousand Island dressing
1000 Families: das Familienalbum des Planeten Erde, a picture book by Uwe Ommer

Music

Thousand Foot Krutch, an alternative rock band
I Feel It/Thousand, a 1993 techno single by Moby
A Thousand Suns, a 2010 album by Linkin Park
A Thousand Years, a 2011 song by Christina Perri
A Thousand Miles, a 2002 song by Vanessa Carlton
A Thousand Answers, a 2012 song by The Hives
1000hp, a 2014 song by Godsmack

Selected numbers in the thousands (1001–1999)

1001–1249

1001 – sphenic number (7 × 11 × 13), pentagonal number, pentatope number

1002 – sphenic number, Mertens function zero, abundant number

1005 – Mertens function zero; first number written in English containing all five vowels a e i o u.

1008 – divisible by the number of primes below it

1009 – smallest four-digit prime, palindromic in bases 11, 15, 19, 24 and 28: (838₁₁, 474₁₅, 2F2₁₉, 1I1₂₄, 181₂₈)

1010 – Mertens function zero

1013 – Sophie Germain prime,^[1] centered square number,^[2] Mertens function zero

1014 – Mertens function zero

1015 – square pyramidal number^[3]

1016 – member of the Mian–Chowla sequence^[4]

1017 – Brick Squad

1018 – Mertens function zero

1019 – Sophie Germain prime,^[1] safe prime^[5]

1020 – polydivisible number

1023 – the highest number one can count to on one's fingers using binary; also the magic number used in Global Positioning System signals

1024 – 2¹⁰, the number of bytes in a kilobyte (in 1999, the IEC coined kibibyte to use for 1024 with kilobyte being 1000, but this convention has not been widely adopted)

1027 – sum of the squares of the first eight primes; can be written from base 2 to base 18 using only the digits 0 to 9.

1028 – sum of totient function for first 58 integers; can be written from base 2 to base 18 using only the digits 0 to 9.

1029 – can be written from base 2 to base 18 using only the digits 0 to 9.

1031 – Sophie Germain prime^[1]

1033 – locale ID of English (United States) in (some version of) Windows.^[6]

1035 – triangular number,^[7] hexagonal number^[8]

1049 – Sophie Germain prime,^[1] highly cototient number^[9]

1051 – centered pentagonal number^[10]

1056 – pronic number^[11]

1060 – sum of the first 25 primes

1071 – heptagonal number^[12]

1072 – centered heptagonal number^[13]

1079 – every positive integer is the sum of at most 1079 tenth powers.

1080 – pentagonal number^[14]

1081 – triangular number,^[7] member of Padovan sequence^[15]

1086 – Smith number,^[16] sum of totient function for first 59 integers

1087 – cousin prime, lucky prime,^[17] Kynea number^[18]

1089 – 33², nonagonal number, centered octagonal number, first natural integer which digits in its decimal expression get reversed when multiplied by 9.^[19]

1091 – cousin prime and twin prime

1092 – divisible by the number of primes below it

1093 – the smallest Wieferich prime (the only other known Wieferich prime is 3511^[20]), twin prime and star number^[21]

1102 – sum of totient function for first 60 integers

1103 – Sophie Germain prime,^[1] balanced prime^[22]

1104 – Keith number^[23]

1105 – Carmichael number,^[24] magic constant of n × n normal magic square and n-queens problem for n = 13, decagonal number,^[25] centered square number,^[2] 1105 = 33² + 4² = 32² + 9² = 31² + 12² = 23² + 24²

1116 – divisible by the number of primes below it

1122 – pronic number,^[11] divisible by the number of primes below it

1123 – balanced prime^[22]

1124 – Leyland number^[26]

1128 – triangular number,^[7] hexagonal number,^[8] divisible by the number of primes below it

1134 - divisible by the number of primes below it

1138 – recurring number in the works of George Lucas and his companies, beginning with his first feature film – THX 1138; particularly, a special code for Easter eggs on Star Wars DVDs.

1140 – tetrahedral number^[27]

1151 – first prime following a prime gap of 22.^[28]

1152 – highly totient number^[29]

1153 – Proth prime^[30]

1156 – 34², octahedral number,^[31] centered pentagonal number,^[10] centered hendecagonal number.^[32]

1159 – member of the Mian–Chowla sequence^[4]

1161 – sum of the first 26 primes

1162 – pentagonal number,^[14] sum of totient function for first 61 integers

1169 – highly cototient number^[9]

1170 – highest possible score in a National Academic Quiz Tournaments (NAQT) match

1176 – triangular number^[7]

1177 – heptagonal number^[12]

1184 – amicable number with 1210^[33]

1187 – safe prime,^[5] Stern prime,^[34] balanced prime^[22]

1190 – pronic number^[11]

1192 – sum of totient function for first 62 integers

1198 – centered heptagonal number^[13]

1200 – the long thousand, ten "long hundreds" of 120 each, the traditional reckoning of large numbers in Germanic languages
the number of households the Nielsen ratings sample^[35]

1201 – centered square number^[2]

1210 – amicable number with 1184^[36]

1216 – nonagonal number^[37]

1217 – Proth prime^[30]

1219 – Mertens function zero

1220 – Mertens function zero

1223 – Sophie Germain prime,^[1] balanced prime^[22]

1225 – 35², triangular number, square triangular number,^[38] hexagonal number,^[8] centered octagonal number^[39]

1228 – sum of totient function for first 63 integers

1229 – Sophie Germain prime,^[1] number of primes between 0 and 10000

1233 – 12² + 33²

1240 – square pyramidal number^[3]

1241 – centered cube number^[40]

1242 – decagonal number^[25]

1247 – pentagonal number^[14]

1249 – emirp, trimorphic number^[41]

1250–1499

1255 – Mertens function zero

1256 – Mertens function zero

1258 – Mertens function zero

1259 – highly cototient number^[9]

1260 – highly composite number,^[42] pronic number,^[11] the smallest vampire number,^[43] sum of totient function for first 64 integers, this number appears twice in the Book of Revelation

1261 – star number,^[21] Mertens function zero

1264 – sum of the first 27 primes

1266 – centered pentagonal number,^[10] Mertens function zero

1270 – Mertens function zero

1275 – triangular number,^[7] sum of the first 50 natural numbers

1279 – Mertens function zero

1280 – Mertens function zero

1282 – Mertens function zero

1283 – safe prime^[5]

1285 – Mertens function zero

1288 – heptagonal number^[12]

1289 – Sophie Germain prime,^[1] Mertens function zero

1291 – Mertens function zero

1292 – Mertens function zero

1296 – 6⁴, 36², sum of the cubes of the first eight positive integers, the number of rectangles on a normal 8 × 8 chessboard

1297 – Mertens function zero

1299 – Mertens function zero

1300 – Sum of the first 4 fifth powers, mertens function zero, largest possible win margin in an NAQT match

1301 – centered square number^[2]

1302 – Mertens function zero

1306 – Mertens function zero. In base 10, raising the digits of 1306 to powers of successive integers equals itself: 1306 = 1¹ + 3² + 0³ + 6⁴. 135, 175, 518, and 598 also have this property.

1307 – safe prime^[5]

1308 – sum of totient function for first 65 integers

1309 – the first sphenic number followed by two consecutive such number

1312 – member of the Mian–Chowla sequence;^[4] code for "ACAB" itself an acronym for "all cops are bastards"^[44]

1318 – Mertens function zero

1319 – safe prime^[5]

1325 – Markov number^[45]

1326 – triangular number,^[7] hexagonal number,^[8] Mertens function zero

1327 – first prime followed by 32 consecutive composite numbers

1328 – sum of totient function for first 66 integers

1329 – Mertens function zero

1330 – tetrahedral number,^[27] forms a Ruth–Aaron pair with 1331 under second definition

1331 – 11³, centered heptagonal number,^[13] forms a Ruth–Aaron pair with 1330 under second definition. This is the only cube of the form x² + x − 1, for x = 36.

1332 – pronic number^[11]

1335 – pentagonal number,^[14] Mertens function zero

1336 – Mertens function zero

1337 – Used in the novel form of spelling called leet

1338 – Mertens function zero

1342 – Mertens function zero

1350 – nonagonal number^[37]

1361 – first prime following a prime gap of 34.^[28]

1365 – pentatope number^[46]

1367 – safe prime,^[5] balanced prime^[22]

1369 – 37², centered octagonal number^[39]

1371 – sum of the first 28 primes

1378 – triangular number^[7]

1379 – magic constant of n × n normal magic square and n-queens problem for n = 14.

1381 – centered pentagonal number^[10]

1387 – 5th Fermat pseudoprime of base 2,^[47] 22nd centered hexagonal number and the 19th decagonal number,^[25] second Super-Poulet number.^[48]

1394 – sum of totient function for first 67 integers

1395 – vampire number,^[43] member of the Mian–Chowla sequence^[4]

1404 – heptagonal number^[12]

1405 – 26² + 27², 7² + 8² + … + 16², centered square number^[2]

1406 – pronic number,^[11] semi-meandric number^[49]

1409 – Sophie Germain prime,^[1] smallest number whose eighth power is the sum of 8 eighth powers, Proth prime^[30]

1419 – Zeisel number^[50]

1425 – self-descriptive number in base 5

1426 – sum of totient function for first 68 integers

1426 – pentagonal number^[14]

1430 – Catalan number^[51]

1431 – triangular number,^[7] hexagonal number^[8]

1432 – member of Padovan sequence^[15]

1433 - Typical port used for remote connections to Microsoft SQL Server databases

1435 – vampire number;^[43] the standard railway gauge in millimetres, equivalent to 4' 8½"

1439 – Sophie Germain prime,^[1] safe prime^[5]

1440 – a highly totient number^[29] and a 481-gonal number. Also, the number of minutes in one day, the blocksize of a standard 3 ¹⁄₂″ floppy disk, and the horizontal resolution of WXGA(II) computer displays

1441 – star number^[21]

1444 – 38², smallest pandigital number in Roman numerals

1451 – Sophie Germain prime^[1]

1458

1469 – octahedral number,^[31] highly cototient number^[9]

1470 – pentagonal pyramidal number,^[52] sum of totient function for first 69 integers

1471 – centered heptagonal number^[13]

1480 – sum of the first 29 primes

1481 – Sophie Germain prime^[1]

1482 – pronic number^[11]

1485 – triangular number

1487 – safe prime^[5]

1490 – tetranacci number^[53]

1491 – nonagonal number,^[37] Mertens function zero

1492 – Mertens function zero

1493 – Stern prime^[34]

1494 – sum of totient function for first 70 integers

1496 – square pyramidal number^[3]

1499 – Sophie Germain prime^[1]

1500–1749

1501 – centered pentagonal number^[10]

1510 –

1511 – Sophie Germain prime,^[1] balanced prime^[22]

1513 – centered square number^[2]

1518 – Mertens function zero

1519 – Mertens function zero

1520 – pentagonal number,^[14] Mertens function zero, forms a Ruth–Aaron pair with 1521 under second definition

1521 – 39², Mertens function zero, centered octagonal number,^[39] forms a Ruth–Aaron pair with 1520 under second definition

1523 – Mertens function zero, safe prime,^[5] member of the Mian–Chowla sequence^[4]

1524 – Mertens function zero

1525 – heptagonal number,^[12] Mertens function zero

1527 – Mertens function zero

1528 – Mertens function zero

1530 – vampire number^[43]

1531 – Mertens function zero

1532 – Mertens function zero

1535 – Thabit number

1537 – Keith number,^[23] Mertens function zero

1540 – triangular number, hexagonal number,^[8] decagonal number,^[25] tetrahedral number^[27]

1543 – Mertens function zero

1544 – Mertens function zero

1546 – Mertens function zero

1556 – sum of the squares of the first nine primes

1559 – Sophie Germain prime^[1]

1560 – pronic number^[11]

1564 – sum of totient function for first 71 integers

1572 – member of the Mian–Chowla sequence^[4]

1575 – odd abundant number^[54]

1583 – Sophie Germain prime

1588 – sum of totient function for first 72 integers

1593 – sum of the first 30 primes

1596 – triangular number

1597 – Fibonacci number,^[55] Markov number,^[45] Prime number, emirp

1600 – 40², repdigit in base 7 (4444₇), street number on Pennsylvania Avenue of the White House, Meters; Common High School Track Event, perfect score on SAT (except from 2005-2015)

1601 – Sophie Germain prime, Proth prime,^[30] the novel 1601 (Mark Twain)

1617 – pentagonal number^[14]

1618 – centered heptagonal number^[13]

1619 – safe prime^[5]

1625 – centered square number^[2]

1626 – centered pentagonal number^[10]

1633 – star number^[21]

1638 – harmonic divisor number^[56]

1639 – nonagonal number^[37]

1640 – pronic number^[11]

1649 – highly cototient number,^[9] Leyland number^[26]

1651 – heptagonal number^[12]

1653 – triangular number, hexagonal number^[8]

1657 – cuban prime^[57]

1660 – sum of totient function for first 73 integers

1666 – largest efficient pandigital number in Roman numerals (each symbol occurs exactly once)

1679 – highly cototient number,^[9] semiprime (23 × 73, see also Arecibo message)

1680 – highly composite number^[42]

1681 – 41², smallest number yielded by the formula n² + n + 41 that is not a prime; centered octagonal number^[39]

1682 – member of a Ruth–Aaron pair (first definition)

1683 – member of a Ruth–Aaron pair (first definition)

1695 – magic constant of n × n normal magic square and n-queens problem for n = 15.

1696 – sum of totient function for first 74 integers

1701 – decagonal number, hull number of the U.S.S. Enterprise on Star Trek

1702 – palindromic in 3 consecutive bases: 898₁₄, 787₁₅, 6A6₁₆

1705 – tribonacci number^[58]

1709 – first of a sequence of eight primes formed by adding 57 in the middle. 1709, 175709, 17575709, 1757575709, 175757575709, 17575757575709, 1757575757575709 and 175757575757575709 are all prime, but 17575757575757575709 = 232433 × 75616446785773

1711 – triangular number

1717 – pentagonal number^[14]

1720 – sum of the first 31 primes

1722 – Giuga number,^[59] pronic number^[11]

1728 – the quantity expressed as 1000 in duodecimal, that is, the cube of twelve (called a great gross), and so, the number of cubic inches in a cubic foot, palindromic in base 11 (1331₁₁) and 23 (363₂₃)

1729 – taxicab number, Carmichael number, Zeisel number, centered cube number, Hardy–Ramanujan number. In the decimal expansion of e the first time all 10 digits appear in sequence starts at the 1729th decimal place. In 1979 the rock musical Hair closed on Broadway in New York City after 1729 performances. Palindromic in bases 12, 32, 36.

1733 – Sophie Germain prime, palindromic in bases 3, 18, 19.

1736 – sum of totient function for first 75 integers

1741 – centered square number^[2]

1747 – balanced prime^[22]

1750–1999

1753 – balanced prime^[22]

1756 – centered pentagonal number^[10]

1760 – the number of yards in a mile

1764 – 42²

1770 – triangular number, hexagonal number,^[8] Town of Seventeen Seventy in Australia

1771 – tetrahedral number^[27]

1772 – centered heptagonal number,^[13] sum of totient function for first 76 integers

1782 – heptagonal number^[12]

1785 – square pyramidal number^[3]

1791 – largest natural number that cannot be expressed as a sum of at most four hexagonal numbers.

1794 – nonagonal number^[37]

1800 – pentagonal pyramidal number,^[52] also, in da Ponte's Don Giovanni, the number of women Don Giovanni had slept with so far when confronted by Donna Elvira, according to Leporello's tally

1801 – cuban prime^[57]

1806 – pronic number,^[11] product of first four terms of Sylvester's sequence, primary pseudoperfect number^[60]

1807 – fifth term of Sylvester's sequence^[61]

1811 – Sophie Germain prime

1820 – pentagonal number,^[14] pentatope number^[46]

1821 – member of the Mian–Chowla sequence^[4]

1823 – safe prime^[5]

1827 – vampire number^[43]

1828 – meandric number, open meandric number

1830 – triangular number

1832 – sum of totient function for first 77 integers

1834 – octahedral number,^[31] sum of the cubes of the first five primes

1836 – factor by which a proton is more massive than an electron

1837 – star number^[21]

1841 – Mertens function zero

1843 – Mertens function zero

1844 – Mertens function zero

1845 – Mertens function zero

1849 – 43², palindromic in base 6 (= 12321₆), centered octagonal number^[39]

1851 – sum of the first 32 primes

1853 – Mertens function zero

1854 – Mertens function zero

1856 – sum of totient function for first 78 integers

1857 – Mertens function zero

1861 – centered square number,^[2] Mertens function zero

1862 – Mertens function zero, forms a Ruth–Aaron pair with 1863 under second definition

1863 – Mertens function zero, forms a Ruth–Aaron pair with 1862 under second definition

1864 – Mertens function zero

1866 – Mertens function zero

1870 – decagonal number^[25]

1885 – Zeisel number^[50]

1889 – Sophie Germain prime, highly cototient number^[9]

1891 – triangular number, hexagonal number,^[8] centered pentagonal number^[10]

1892 – pronic number^[11]

1896 – member of the Mian–Chowla sequence^[4]

1897 – member of Padovan sequence^[15]

1900 – 1900 (film) or Novecento, 1977 movie

1901 – Sophie Germain prime

1907 – safe prime,^[5] balanced prime^[22]

1909 – hyperperfect number^[62]

1918 – heptagonal number^[12]

1926 – pentagonal number^[14]

1929 – Mertens function zero

1931 – Sophie Germain prime

1933 – centered heptagonal number,^[13] prime number

1934 – sum of totient function for first 79 integers

1936 – 44², 18-gonal number,^[63] 324-gonal number.

1938 – Mertens function zero

1951 – cuban prime^[57]

1953 – triangular number

1956 – nonagonal number^[37]

1966 – sum of totient function for first 80 integers

1969 - Only value less than four million for which a "mod-ification" of the standard Ackermann Function does not stabilize ^[64]

1973 – Sophie Germain prime

1980 – pronic number^[11]

1984 – 11111000000 in binary, see also: 1984 (disambiguation)

1985 – centered square number^[2]

1987 – 300th prime number

1988 – sum of the first 33 primes

References

Wikimedia Commons has media related to 1000 (number).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 "Sloane's A005384 : Sophie Germain primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 6 7 8 9 10 "Sloane's A001844 : Centered square numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 "Sloane's A000330 : Square pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 6 7 8 "Sloane's A005282 : Mian-Chowla sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 6 7 8 9 10 11 12 "Sloane's A005385 : Safe primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ .
1 2 3 4 5 6 7 8 "Sloane's A000217 : Triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 6 7 8 9 "Sloane's A000384 : Hexagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 6 7 "Sloane's A100827 : Highly cototient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 6 7 8 "Sloane's A005891 : Centered pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 6 7 8 9 10 11 12 13 "Sloane's A002378 : Oblong (or promic, pronic, or heteromecic) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 6 7 8 "Sloane's A000566 : Heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 6 7 "Sloane's A069099 : Centered heptagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 6 7 8 9 10 "Sloane's A000326 : Pentagonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 "Sloane's A000931 : Padovan sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A006753 : Smith numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A031157 : Numbers that are both lucky and prime". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A093069 : a(n) = (2^n + 1)^2 - 2". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A001232 : Numbers n such that 9*n = (n written backwards)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-14.
↑ Wells, D. The Penguin Dictionary of Curious and Interesting Numbers London: Penguin Group. (1987): 163
1 2 3 4 5 "Sloane's A003154 : Centered 12-gonal numbers. Also star numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 6 7 8 9 "Sloane's A006562 : Balanced primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 "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.
1 2 3 4 5 "Sloane's A001107 : 10-gonal (or decagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 "Sloane's A076980 : Leyland numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 "Sloane's A000292 : Tetrahedral numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 "Sloane's A000101 : Increasing gaps between primes (upper end)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-07-10.
1 2 "Sloane's A097942 : Highly totient numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 "Sloane's A080076 : Proth primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 "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.
↑ Higgins, Peter (2008). Number Story: From Counting to Cryptography. New York: Copernicus. p. 61. ISBN 978-1-84800-000-1.
1 2 "Sloane's A042978 : Stern primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ Meehan, Eileen R., Why TV is not our fault: television programming, viewers, and who's really in control Lanham, MD: Rowman & Littlefield, 2005
↑ Higgins, ibid.
1 2 3 4 5 6 "Sloane's A001106 : 9-gonal (or enneagonal or nonagonal) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A001110 : Square triangular numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 "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's A005898 : Centered cube numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A033819 : Trimorphic numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 "Sloane's A002182 : Highly composite numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 4 5 "Sloane's A014575 : Vampire numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Constitutional Court allows 'FCK CPS' sticker". 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.
1 2 "Sloane's A002559 : Markoff (or Markov) numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 "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'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's A000682 : Semimeanders". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 "Sloane's A051015 : Zeisel numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A000108 : Catalan numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 "Sloane's A002411 : Pentagonal pyramidal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A000078 : Tetranacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A005231 : Odd abundant numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A000045 : Fibonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A001599 : Harmonic or Ore numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
1 2 3 "Sloane's A002407 : Cuban primes". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A000073 : Tribonacci numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A007850 : Giuga numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A054377 : Primary pseudoperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A000058 : Sylvester's sequence". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A034897 : Hyperperfect numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ "Sloane's A051870 : 18-gonal numbers". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2016-06-12.
↑ 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. JSTOR 2323780.

Large numbers

Examples in numerical order

Expression methods

Notations	Knuth's up-arrow notation Conway chained arrow notation Steinhaus–Moser notation

Operators	Hyperoperation Tetration Pentation Ackermann function Bowers' operators

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