100,000
| ||||
---|---|---|---|---|
Cardinal | one hundred thousand | |||
Ordinal | 100000th (one hundred thousandth) | |||
Factorization | 25 × 55 | |||
Greek numeral | ||||
Roman numeral | C | |||
Binary | 110000110101000002 | |||
Ternary | 120020112013 | |||
Senary | 20505446 | |||
Octal | 3032408 | |||
Duodecimal | 49A5412 | |||
Hexadecimal | 186A016 | |||
Egyptian hieroglyph | 𓆐 |
100,000 (one hundred thousand) is the natural number following 99,999 and preceding 100,001. In scientific notation, it is written as 105.
Terms for 100,000[edit]
In Bangladesh, India, Pakistan and South Asia, one hundred thousand is called a lakh, and is written as 1,00,000. The Thai, Lao, Khmer and Vietnamese languages also have separate words for this number: แสน, ແສນ, សែន (all saen), and ức respectively. The Malagasy word is hetsy.[1]
In Cyrillic numerals, it is known as the legion (легион): or .
Values of 100,000[edit]
In astronomy, 100,000 metres, 100 kilometres, or 100 km (62 miles) is the altitude at which the Fédération Aéronautique Internationale (FAI) defines spaceflight to begin.
In paleoclimatology, the 100,000-year problem is a mismatch between the temperature record and the modeled incoming solar radiation.
In the Irish language, céad míle fáilte (pronounced [ˌceːd̪ˠ ˈmʲiːlʲə ˈfˠaːl̠ʲtʲə]) is a popular greeting meaning "a hundred thousand welcomes".
Selected 6-digit numbers (100,001–999,999)[edit]
100,001 to 199,999[edit]
- 100,003 = smallest 6-digit prime number[2]
- 100,128 = smallest triangular number with 6 digits and the 447th triangular number
- 100,151 = twin prime with 100,153
- 100,153 = twin prime with 100,151
- 100,255 = Friedman number[3]
- 100,489 = 3172, the smallest 6-digit square
- 101,101 = smallest palindromic Carmichael number
- 101,723 = smallest prime number whose square is a pandigital number containing each digit from 0 to 9
- 102,564 = The smallest parasitic number
- 103,049 = Schröder–Hipparchus number[4]
- 103,680 = highly totient number[5]
- 103,769 = the number of combinatorial types of 5-dimensional parallelohedra
- 103,823 = 473, the smallest 6-digit cube and nice Friedman number (−1 + 0 + 3×8×2)3
- 104,480 = number of non-isomorphic set-systems of weight 14.
- 104,723 = the 9,999th prime number
- 104,729 = the 10,000th prime number
- 104,869 = the smallest prime number containing every non-prime digit
- 104,976 = 184, 3-smooth number
- 105,071 = number of triangle-free graphs on 11 vertices[6]
- 105,558 = number of partitions of 46[7]
- 105,664 = harmonic divisor number[8]
- 108,968 = number of signed trees with 11 nodes[9]
- 109,376 = automorphic number[10]
- 110,880 = highly composite number[11]
- 111,111 = repunit
- 111,777 = smallest natural number requiring 17 syllables in American English, 19 in British English
- 113,634 = Motzkin number for n = 14[12]
- 114,243/80,782 ≈ √2
- 114,689 = prime factor of F12
- 115,975 = Bell number[13]
- 116,281 = 3412, square number, centered decagonal number, 18-gonal number
- 117,067 = first vampire prime
- 117,649 = 76
- 117,800 = harmonic divisor number[8]
- 120,032 = number of primitive polynomials of degree 22 over GF(2)[14]
- 120,284 = Keith number[15]
- 120,960 = highly totient number[5]
- 121,393 = Fibonacci number[16]
- 123,717 = smallest digitally balanced number in base 7[17]
- 123,867 = number of trees with 18 unlabeled nodes[18]
- 124,754 = number of partitions of 47[7]
- 125,673 = logarithmic number[19]
- 127,777 = smallest natural number requiring 18 syllables in American English, 20 in British English
- 127,912 = Wedderburn–Etherington number[20]
- 128,981 = Starts the first prime gap sequence of 2, 4, 6, 8, 10, 12, 14
- 129,106 = Keith number[15]
- 130,321 = 194
- 131,071 = Mersenne prime[21]
- 131,072 = 217 and largest determinant of a (real) {0,1}-matrix of order 15.[22]
- 131,361 = Leyland number[23]
- 134,340 = Pluto's minor planet designation
- 135,135 = double factorial of 13
- 135,137 = Markov number[24]
- 142,129 = 3772, square number, dodecagonal number
- 142,857 = Kaprekar number, smallest cyclic number in decimal.
- 144,000 = number with religious significance
- 147,273 = number of partitions of 48[7]
- 147,640 = Keith number[15]
- 148,149 = Kaprekar number[25]
- 152,381 = unique prime in base 20
- 156,146 = Keith number[15]
- 155,921 = smallest prime number being the only prime in an interval from 100n to 100n + 99
- 160,000 = 204
- 160,176 = number of reduced trees with 26 nodes[26]
- 161,051 = 115
- 161,280 = highly totient number[5]
- 166,320 = highly composite number[11]
- 167,400 = harmonic divisor number[8]
- 167,894 = number of ways to partition {1,2,3,4,5,6,7,8} and then partition each cell (block) into subcells.[27]
- 173,525 = number of partitions of 49[7]
- 173,600 = harmonic divisor number[8]
- 174,680 = Keith number[15]
- 174,763 = Wagstaff prime[28]
- 176,906 = number of 24-bead necklaces (turning over is allowed) where complements are equivalent[29]
- 177,147 = 311
- 177,777 = smallest natural number requiring 19 syllables in American English, 21 in British English
- 178,478 = Leyland number[23]
- 181,440 = highly totient number[5]
- 181,819 = Kaprekar number[25]
- 182,362 = number of 23-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[30]
- 183,186 = Keith number[15]
- 183,231 = number of partially ordered set with 9 unlabeled elements[31]
- 187,110 = Kaprekar number[25]
- 189,819 = number of letters in the longest English word, taking 3 hours to pronounce[32]
- 194,481 = 214
- 195,025 = Pell number,[33] Markov number[24]
- 196,418 = Fibonacci number,[16] Markov number[24]
- 196,560 = the kissing number in 24 dimensions
- 196,883 = the dimension of the smallest nontrivial irreducible representation of the Monster group
- 196,884 = the coefficient of q in the Fourier series expansion of the j-invariant. The adjacency of 196883 and 196884 was important in suggesting monstrous moonshine.
- 199,999 = prime number.
200,000 to 299,999[edit]
- 202,717 = k such that the sum of the squares of the first k primes is divisible by k.[34]
- 206,098 – Large Schröder number
- 206,265 = rounded number of arc seconds in a radian (see also parsec), since 180 × 60 × 60/π = 206,264.806...
- 207,360 = highly totient number[5]
- 208,012 = the Catalan number C12[35]
- 208,335 = the largest number to be both triangular and square pyramidal[36]
- 208,495 = Kaprekar number[25]
- 212,159 = smallest unprimeable number ending in 1, 3, 7 or 9[37][38]
- 221,760 = highly composite number[11]
- 222,222 = repdigit
- 224,737 = the 20,000th prime number
- 227,475 = Riordan number
- 234,256 = 224
- 237,510 = harmonic divisor number[8]
- 238,591 = number of free 13-ominoes
- 241,920 = highly totient number[5]
- 242,060 = harmonic divisor number[8]
- 248,832 = 125, 100,00012, AKA a gross-great-gross (10012 great-grosses); the smallest fifth power that can be represented as the sum of only 6 fifth powers: 125 = 45 + 55 + 65 + 75 + 95 + 115
- 255,168 = number of ways to play tic tac toe[39]
- 262,144 = 218; exponential factorial of 4;[40] a superperfect number[41]
- 262,468 = Leyland number[23]
- 268,705 = Leyland number[23]
- 274,177 = prime factor of the Fermat number F6
- 275,807/195,025 ≈ √2
- 276,480 = number of primitive polynomials of degree 24 over GF(2)[14]
- 277,200 = highly composite number[11]
- 279,841 = 234
- 279,936 = 67
- 280,859 = a prime number whose square 78881777881 is tridigital
- 291,400 = number of non-equivalent ways of expressing 100,000,000 as the sum of two prime numbers[42]
- 293,547 = Wedderburn–Etherington number[20]
- 294,001 = smallest weakly prime number in base 10[43]
- 294,685 = Markov number[24]
- 298,320 = Keith number[15]
300,000 to 399,999[edit]
- 310,572 = Motzkin number[12]
- 314,159 = pi-prime
- 316,749 = number of reduced trees with 27 nodes[26]
- 317,811 = Fibonacci number[16]
- 317,955 = number of trees with 19 unlabeled nodes[44]
- 318,682 = Kaprekar number[25]
- 325,878 = Fine number[45]
- 326,981 = alternating factorial[46]
- 329,967 = Kaprekar number[25]
- 331,776 = 244
- 332,640 = highly composite number;[11] harmonic divisor number[8]
- 333,333 = repdigit
- 333,667 = sexy prime and unique prime[47]
- 333,673 = sexy prime with 333,679
- 333,679 = sexy prime with 333,673
- 337,500 = 22 × 33 × 55
- 337,594 = number of 25-bead necklaces (turning over is allowed) where complements are equivalent[29]
- 349,716 = number of 24-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[30]
- 351,351 = only known odd abundant number that is not the sum of some of its proper, nontrivial (i.e. >1) divisors (sequence A122036 in the OEIS).
- 351,352 = Kaprekar number[25]
- 355,419 = Keith number[15]
- 356,643 = Kaprekar number[25]
- 356,960 = number of primitive polynomials of degree 23 over GF(2)[14]
- 360,360 = harmonic divisor number;[8] the smallest number divisible by the numbers from 1 to 15 (there is no smaller number divisible by the numbers from 1 to 14 since any number divisible by 3 and 5 must also be divisible by 15)
- 362,880 = 9!, highly totient number[5]
- 369,119 = prime number which divides the sum of all primes less than or equal to it[48]
- 369,293 = smallest prime with the property that inserting a digit anywhere in the number will always yield a composite[49]
- 370,261 = first prime followed by a prime gap of over 100
- 371,293 = 135, palindromic in base 12 (15AA5112)
- 385,321 = Acid-Notation prime
- 386,051 = another Acid-Notation prime
- 389,305 = self-descriptive number in base 7
- 390,313 = Kaprekar number[25]
- 390,625 = 58
- 397,585 = Leyland number[23]
400,000 to 499,999[edit]
- 409,113 = sum of the first nine factorials
- 422,481 = smallest number whose fourth power is the sum of three smaller fourth powers
- 423,393 = Leyland number[23]
- 426,389 = Markov number[24]
- 426,569 = cyclic number in base 12
- 437,760 to 440,319 = any of these numbers will cause the Apple II+ and Apple IIe computers to crash to a monitor prompt when entered at the BASIC prompt, due to a short-cut in the Applesoft code programming of the overflow test when evaluating 16-bit numbers.[50] Entering 440000 at the prompt has been used to hack games that are protected against entering commands at the prompt after the game is loaded.
- 444,444 = repdigit
- 456,976 = 264
- 461,539 = Kaprekar number[25]
- 466,830 = Kaprekar number[25]
- 470,832 = Pell number[33]
- 483,840 = highly totient number[5]
- 492,638 = number of signed trees with 12 nodes[51]
- 498,960 = highly composite number[11]
- 499,393 = Markov number[24]
- 499,500 = Kaprekar number[25]
500,000 to 599,999[edit]
- 500,500 = Kaprekar number,[25] sum of first 1,000 integers
- 509,203 = Riesel number[52]
- 510,510 = the product of the first seven prime numbers, thus the seventh primorial.[53] It is also the product of four consecutive Fibonacci numbers—13, 21, 34, 55, the largest such sequence of any length to be also a primorial. And it is a double triangular number, the sum of all even numbers from 0 to 1428.
- 514,229 = Fibonacci prime,[54]
- 518,859 = Schröder–Hipparchus number[4]
- 524,287 = Mersenne prime[21]
- 524,288 = 219
- 524,649 = Leyland number[23]
- 525,600 = minutes in a non-leap year
- 527,040 = minutes in a leap year
- 531,441 = 312
- 533,169 = Leyland number[23]
- 533,170 = Kaprekar number[25]
- 537,824 = 145
- 539,400 = harmonic divisor number[8]
- 548,834 = equal to the sum of the sixth powers of its digits
- 554,400 = highly composite number[11]
- 555,555 = repdigit
- 586,081 = number of prime numbers having seven digits.[55]
- 593,661 = the ID of the most commonly used custom song in Geometry Dash (Xtrullor - Supernova)
- 599,999 = prime number.
600,000 to 699,999[edit]
- 604,800 = number of seconds in a week
- 614,656 = 284
- 625,992 = Riordan number
- 629,933 = number of reduced trees with 28 nodes[26]
- 645,120 = double factorial of 14
- 646,018 = Markov number[24]
- 649,532 = number of 26-bead necklaces (turning over is allowed) where complements are equivalent[29]
- 664,579 = the number of primes under 10,000,000
- 665,280 = highly composite number[11]
- 665,857/470,832 ≈ √2
- 666,666 = repdigit
- 671,092 = number of 25-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed[30]
- 676,157 = Wedderburn–Etherington number[20]
- 678,570 = Bell number[13]
- 694,280 = Keith number[15]
- 695,520 = harmonic divisor number[8]
700,000 to 799,999[edit]
- 700,001 = prime number.
- 707,281 = 294
- 720,720 = superior highly composite number;[56] colossally abundant number;[57] the smallest number divisible by the numbers from 1 to 16
- 725,760 = highly totient number[5]
- 726,180 = harmonic divisor number[8]
- 729,000 = 903
- 739,397 = largest prime that is both right- and left-truncatable.
- 742,900 = Catalan number[35]
- 753,480 = harmonic divisor number[8]
- 759,375 = 155
- 765,623 = emirp, Friedman prime 56 × 72 − 6 ÷ 3
- 777,777 = repdigit, smallest natural number requiring 20 syllables in American English, 22 in British English, largest number in English not containing the letter 'i' in its name
- 783,700 = initial number of third century xx00 to xx99 (after 400 and 1,400) containing seventeen prime numbers[58][a] {783,701, 783,703, 783,707, 783,719, 783,721, 783,733, 783,737, 783,743, 783,749, 783,763, 783,767, 783,779, 783,781, 783,787, 783,791, 783,793, 783,799}
- 799,999 = prime number.
800,000 to 899,999[edit]
- 810,000 = 304
- 823,065 = number of trees with 20 unlabeled nodes[60]
- 823,543 = 77
- 825,265 = smallest Carmichael number with 5 prime factors
- 832,040 = Fibonacci number[16]
- 853,467 = Motzkin number[12]
- 857,375 = 953
- 873,612 = 11 + 22 + 33 + 44 + 55 + 66 + 77
- 888,888 = repdigit
- 890,625 = automorphic number[10]
900,000 to 999,999[edit]
- 900,001 = prime number
- 901,971 = number of free 14-ominoes
- 909,091 = unique prime in base 10
- 923,521 = 314
- 925,765 = Markov number[24]
- 925,993 = Keith number[15]
- 950,976 = harmonic divisor number[8]
- 956,619: 956619^2=915119911161, and only the digits 1, 5, 6 and 9 are used in both this number and its square.
- 967,680 = highly totient number[5]
- 970,299 = 993, the largest 6-digit cube
- 998,001 = 9992, the largest 6-digit square. The reciprocal of this number, in its expanded form, lists all three-digit numbers in order except 998.[61]
- 998,991 = largest triangular number with 6 digits and the 1413th triangular number
- 999,983 = largest 6-digit prime number
- 999,999 = repdigit. Rational numbers with denominators 7 and 13 have 6-digit repetends when expressed in decimal form, because 999999 is the smallest number one less than a power of 10 that is divisible by 7 and by 13, and it is the largest number in English not containing the letter 'l' in its name.
Prime numbers[edit]
There are 9,592 primes less than 105, where 99,991 is the largest prime number smaller than 100,000.
Increments of 105 from 100,000 through a one million have the following prime counts:
- 8,392 primes between 100,000 and 200,000.[b] This is a difference of 1,200 primes from the previous range.
- 104,729 is the 10,000th prime in this range.
- 199,999 is prime.
- 8,013 primes between 200,000 and 300,000.[c] A difference of 379 primes from the previous range.
- 224,737 is the 20,000th prime.
- 7,863 primes between 300,000 and 400,000.[d] A difference of 150 primes from the previous range.
- 350,377 is the 30,000th prime.
- 7,678 primes between 400,000 and 500,000.[e] A difference of 185 primes from the previous range. Here, the difference increases by a count of 35.
- 479,909 is the 40,000th prime.
- 7,560 primes between 500,000 and 600,000.[f] A difference of 118 primes from the previous range.
- 7,445 primes between 600,000 and 700,000.[g] A difference of 115 primes from the previous range.
- 611,953 is the 50,000th prime.
- 7,408 primes between 700,000 and 800,000.[h] A difference of 37 primes from the previous range.
- 700,001 and 799,999 are both prime.
- 746,773 is the 60,000th prime.
- 7,323 primes between 800,000 and 900,000.[i] A difference of 85 primes from the previous range. Here, the difference increases by a count of 48.
- 882,377 is the 70,000th prime.
- 7,224 primes between 900,000 and 1,000,000.[j] A difference of 99 primes from the previous range. The difference increases again, by a count of 14.
- 900,001 is prime.
In total, there are 68,906 prime numbers between 100,000 and 1,000,000.[62]
Notes[edit]
- ^ There are no centuries containing more than seventeen primes between 200 and 122,853,771,370,899 inclusive.[59]
- ^ Smallest p > 100,000 is 100,003 (9,593rd); largest p < 200,000 is 199,999 (17,984th).
- ^ Smallest p > 200,000 is 200,003 (17,985th); largest p < 300,000 is 299,993 (25,997th).
- ^ Smallest p > 300,000 is 300,007 (25,998th); largest p < 400,000 is 399,989 (33,860th).
- ^ Smallest p > 400,000 is 400,009 (33,861st); largest p < 500,000 is 499,979 (41,538th).
- ^ Smallest p > 500,000 is 500,009 (41,539th); largest p < 600,000 is 599,999 (49,098th).
- ^ Smallest p > 600,000 is 600,011 (49,099th); largest p < 700,000 is 699,967 (56,543rd).
- ^ Smallest p > 700,000 is 700,001 (56,544th); largest p < 800,000 is 799,999 (63,951st).
- ^ Smallest p > 800,000 is 800,011 (63,952nd); largest p < 900,000 is 899,981 (71,274th).
- ^ Smallest p > 900,000 is 900,001 (71,275th); largest p < 1,000,000 is 999,983 (78,498th).
References[edit]
- ^ "Malagasy Dictionary and Madagascar Encyclopedia : hetsy". malagasyword.org. 26 October 2017. Retrieved 2019-12-31.
- ^ Sloane, N. J. A. (ed.). "Sequence A003617 (Smallest n-digit prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Problem of the Month (August 2000)". Archived from the original on 2012-12-18. Retrieved 2013-01-13.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A001003 (Schroeder's second problem (generalized parentheses); also called super-Catalan numbers or little Schroeder numbers.)". 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 A097942 (Highly totient numbers)". 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.
- ^ a b c d 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.
- ^ a b c d e f g h i j k l m Sloane, N. J. A. (ed.). "Sequence A001599 (Harmonic or Ore numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000060 (Number of signed trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A003226 (Automorphic numbers: m^2 ends with m)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i Sloane, N. J. A. (ed.). "Sequence A002182 (Highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A001006 (Motzkin numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000110 (Bell or exponential numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A011260 (Number of primitive polynomials of degree n over GF(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 A007629 (Repfigit (REPetitive FIbonacci-like diGIT) numbers (or Keith numbers))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d Sloane, N. J. A. (ed.). "Sequence A000045 (Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A049363 (a(1) = 1; for n > 1, smallest digitally balanced number in base n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000055 (Number of trees with n unlabeled nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002104 (Logarithmic numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A001190 (Wedderburn-Etherington numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000668 (Mersenne primes (primes of the form 2^n - 1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A003432 (Hadamard maximal determinant problem)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation. Retrieved 2024-03-30.
- ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A076980 (Leyland numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h Sloane, N. J. A. (ed.). "Sequence A002559 (Markoff (or Markov) numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c d e f g h i j k l m n Sloane, N. J. A. (ed.). "Sequence A006886 (Kaprekar numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c 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 A000258 (Expansion of e.g.f. exp(exp(exp(x)-1)-1))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000979 (Wagstaff primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A000011 (Number of n-bead necklaces (turning over is allowed) where complements are equivalent)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b c Sloane, N. J. A. (ed.). "Sequence A000013 (Definition (1): Number of n-bead binary necklaces with beads of 2 colors where the colors may be swapped but turning over is not allowed)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000112 (Number of partially ordered sets (posets) with n unlabeled elements)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "The longest word in English? Here are the top 15 biggest ones". Berlitz. Retrieved 2024-03-01.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000129 (Pell numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A111441 (Numbers k such that the sum of the squares of the first k primes is divisible by k)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ a b Sloane, N. J. A. (ed.). "Sequence A000108 (Catalan numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000330 (Square pyramidal numbers: a(n) = 0^2 + 1^2 + 2^2 + ... + n^2 = n*(n+1)*(2*n+1)/6)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Collins, Julia (2019). Numbers in Minutes. United Kingdom: Quercus. p. 140. ISBN 978-1635061772.
- ^ Sloane, N. J. A. (ed.). "Sequence A143641 (Odd prime-proof numbers not ending in 5)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "How many Tic-Tac-Toe (Noughts and crosses) games?".
- ^ Sloane, N. J. A. (ed.). "Sequence A049384 (a(0)=1, a(n+1) = (n+1)^a(n))". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A019279 (Superperfect numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A065577 (Number of Goldbach partitions of 10^n)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Weißstein, Eric W. (25 December 2020). "Weakly Prime". Wolfram MathWorld.
- ^ Sloane, N. J. A. (ed.). "Sequence A000055 (Number of trees with n unlabeled nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000957 (Fine's sequence (or Fine numbers): number of relations of valence greater than or equal to 1 on an n-set; also number of ordered rooted trees with n edges having root of even degree)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005165 (Alternating factorials)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A040017 (Unique period primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A007506 (Primes p with property that p divides the sum of all primes <= p)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A125001 (Non-insertable primes: primes with property that no matter where you insert (or prepend or append) a digit you get a composite number (except for prepending a zero).)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Applesoft Disassembly -- S.d912". Archived from the original on 2016-04-15. Retrieved 2016-04-04. Disassembled ROM. See comments at $DA1E.
- ^ Sloane, N. J. A. (ed.). "Sequence A000060 (Number of signed trees with n nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A101036 (Riesel numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002110 (Primorial numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A005478 (Prime Fibonacci numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.Sloane, N. J. A. (ed.). "Sequence A178444 (Markov numbers that are prime)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A006879 (Number of primes with n digits.)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A002201 (Superior highly composite numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A004490 (Colossally abundant numbers)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A186509 (Centuries containing 17 primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A186311 (Least century 100k to 100k+99 with exactly n primes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ Sloane, N. J. A. (ed.). "Sequence A000055 (Number of trees with n unlabeled nodes)". The On-Line Encyclopedia of Integer Sequences. OEIS Foundation.
- ^ "Dividing one by 998001 produces list of three digit numbers". 23 January 2012.
- ^ Caldwell, Chris K. "The Nth Prime Page". PrimePages. Retrieved 2022-12-03. From the differences of the prime indexes of the smallest and largest prime numbers in ranges of increments of 105, plus 1 (for each range).