cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-9 of 9 results.

A255922 Bases b for which exactly one Wieferich prime p with p < b exists such that p is a base-b Wieferich prime.

Original entry on oeis.org

5, 7, 8, 9, 10, 13, 21, 22, 23, 24, 25, 27, 29, 30, 31, 32, 33, 35, 38, 42, 43, 44, 45, 46, 48, 50, 54, 55, 60, 61, 64, 70, 74, 77, 78, 79, 85, 91, 94, 98, 100, 105, 110, 112, 113, 115, 120, 122, 126, 128, 131, 132, 133, 136, 138, 141, 150, 151, 152, 153, 154
Offset: 1

Views

Author

Felix Fröhlich, Mar 12 2015

Keywords

Comments

Numbers b such that A255920(n) = 1.

Links

Crossrefs

Cf. A255920.
Cf. bases b with exactly k base-b Wieferich primes less than b: A255921 (k=0), A255923 (k=2), A255924 (k=3), A255925 (k=4), A325881 (k=5), A325882 (k=6), A325883 (k=7), A325884 (k=8), A325885 (k=9), A325886 (k=10).

Programs

  • PARI
    is(n) = my(i=0); forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, i++); if(i > 1, return(0))); i==1

A255923 Bases b for which exactly two Wieferich primes p with p < b exist such that p is a base-b Wieferich prime.

Original entry on oeis.org

17, 18, 26, 37, 40, 41, 49, 51, 57, 62, 63, 65, 67, 69, 71, 73, 75, 76, 81, 82, 93, 97, 101, 109, 121, 124, 125, 127, 130, 134, 149, 157, 164, 165, 168, 172, 174, 179, 188, 190, 193, 195, 199, 201, 202, 206, 207, 214, 217, 218, 221, 229, 235, 236, 239, 241
Offset: 1

Views

Author

Felix Fröhlich, Mar 23 2015

Keywords

Comments

Numbers b such that A255920(b) = 2.

Links

Crossrefs

Cf. A255920.
Cf. bases b with exactly k base-b Wieferich primes less than b: A255921 (k=0), A255922 (k=1), A255924 (k=3), A255925 (k=4), A325881 (k=5), A325882 (k=6), A325883 (k=7), A325884 (k=8), A325885 (k=9), A325886 (k=10).

Programs

  • PARI
    is(n) = my(i=0); forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, i++); if(i > 2, return(0))); i==2
  • Sage
    [b for b in range(3,242) if len([p for p in range(2,b) if is_prime(p) and mod(b, p^2)^(p-1)==1])==2] # Danny Rorabaugh, Mar 31 2015

A255924 Bases b for which exactly three Wieferich primes p with p < b exist such that p is a base-b Wieferich prime.

Original entry on oeis.org

19, 28, 53, 68, 80, 89, 107, 129, 137, 143, 145, 146, 147, 148, 170, 177, 181, 197, 215, 224, 253, 263, 268, 299, 307, 324, 332, 333, 334, 339, 341, 349, 350, 354, 357, 359, 360, 362, 368, 373, 377, 389, 393, 399, 402, 403, 410, 413, 437, 440, 449, 451, 457
Offset: 1

Views

Author

Felix Fröhlich, Mar 23 2015

Keywords

Comments

Numbers b such that A255920(b) = 3.

Links

Crossrefs

Cf. A255920.
Cf. bases b with exactly k base-b Wieferich primes less than b: A255921 (k=0), A255922 (k=1), A255923 (k=2), A255925 (k=4), A325881 (k=5), A325882 (k=6), A325883 (k=7), A325884 (k=8), A325885 (k=9), A325886 (k=10).

Programs

  • PARI
    is(n) = my(i=0); forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, i++); if(i > 3, return(0))); i==3
  • Sage
    [b for b in range(3, 458) if len([p for p in range(2, b) if is_prime(p) and mod(b, p^2)^(p-1)==1])==3] # Danny Rorabaugh, Mar 31 2015

A255925 Bases b for which exactly four Wieferich primes p with p < b exist such that p is a base-b Wieferich prime.

Original entry on oeis.org

116, 117, 118, 233, 245, 249, 251, 261, 269, 276, 298, 325, 369, 374, 401, 423, 460, 485, 487, 505, 526, 604, 618, 629, 653, 717, 721, 723, 737, 776, 793, 838, 851, 856, 857, 863, 867, 881, 893, 932, 962, 969, 978, 1025, 1037, 1045, 1057, 1059, 1079, 1106
Offset: 1

Views

Author

Felix Fröhlich, Mar 23 2015

Keywords

Comments

Numbers b such that A255920(b) = 4.

Links

Crossrefs

Cf. A255920.
Cf. bases b with exactly k base-b Wieferich primes less than b: A255921 (k=0), A255922 (k=1), A255923 (k=2), A255924 (k=3), A325881 (k=5), A325882 (k=6), A325883 (k=7), A325884 (k=8), A325885 (k=9), A325886 (k=10).

Programs

  • Mathematica
    wp[b_] := Count[Complement[Prime[Range[PrimePi[b]]], FactorInteger[b][[All, 1]] ], p_ /; Divisible[b^(p - 1) - 1, p^2]];
Select[Range[2, 1200], wp[#] == 4&] (* Jean-François Alcover, Nov 26 2017 *)
  • PARI
    is(n) = my(i=0); forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, i++); if(i > 4, return(0))); i==4
  • Sage
    [b for b in range(3,1107) if len([p for p in range(2,b) if is_prime(p) and mod(b, p^2)^(p-1)==1])==4] # Danny Rorabaugh, Mar 31 2015

A325881 Bases b where exactly five primes p with p < b exist such that p is a base-b Wieferich prime.

Original entry on oeis.org

99, 161, 226, 293, 313, 424, 521, 557, 577, 606, 632, 649, 753, 757, 821, 874, 901, 925, 937, 1030, 1033, 1081, 1108, 1116, 1149, 1342, 1443, 1457, 1524, 1549, 1557, 1586, 1618, 1668, 1777, 1921, 1927, 1929, 1993, 2039, 2060, 2061, 2069, 2077, 2098, 2141, 2269
Offset: 1

Views

Author

Felix Fröhlich, May 26 2019

Keywords

Comments

Numbers n such that A255920(n) = 5.

Crossrefs

Cf. A255920.
Cf. bases b with exactly k base-b Wieferich primes less than b: A255921 (k=0), A255922 (k=1), A255923 (k=2), A255924 (k=3), A255925 (k=4), A325882 (k=6), A325883 (k=7), A325884 (k=8), A325885 (k=9), A325886 (k=10).

Programs

  • PARI
    is(n) = my(i=0); forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, i++)); i==5

A325882 Bases b where exactly six primes p with p < b exist such that p is a base-b Wieferich prime.

Original entry on oeis.org

361, 476, 699, 977, 1121, 1145, 1293, 1667, 1745, 1868, 2157, 2382, 2468, 2665, 2793, 2897, 3038, 3149, 3526, 4033, 4643, 4746, 4789, 5032, 5073, 5567, 5651, 5660, 5777, 5824, 6205, 6320, 6346, 6377, 6421, 6732, 6769, 6949, 6957, 6976, 7318, 7669, 7793, 7937
Offset: 1

Views

Author

Felix Fröhlich, May 26 2019

Keywords

Comments

Numbers n such that A255920(n) = 6.

Crossrefs

Cf. A255920.
Cf. bases b with exactly k base-b Wieferich primes less than b: A255921 (k=0), A255922 (k=1), A255923 (k=2), A255924 (k=3), A255925 (k=4), A325881 (k=5), A325883 (k=7), A325884 (k=8), A325885 (k=9), A325886 (k=10).

Programs

  • PARI
    is(n) = my(i=0); forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, i++)); i==6

A325883 Bases b where exactly seven primes p with p < b exist such that p is a base-b Wieferich prime.

Original entry on oeis.org

1451, 1482, 3145, 3147, 3277, 3365, 3376, 4339, 4357, 4365, 4393, 4625, 5649, 5850, 7282, 7624, 8641, 8956, 8957, 9149, 9449, 10040, 10093, 10538, 10835, 10889, 12001, 12476, 12907, 13253, 14005, 14027, 14032, 14500, 15029, 15229, 15797, 15857, 16249, 16757
Offset: 1

Views

Author

Felix Fröhlich, May 26 2019

Keywords

Comments

Numbers n such that A255920(n) = 7.

Crossrefs

Cf. A255920.
Cf. bases b with exactly k base-b Wieferich primes less than b: A255921 (k=0), A255922 (k=1), A255923 (k=2), A255924 (k=3), A255925 (k=4), A325881 (k=5), A325882 (k=6), A325884 (k=8), A325885 (k=9), A325886 (k=10).

Programs

  • PARI
    is(n) = my(i=0); forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, i++)); i==7

A325885 Bases b where exactly nine primes p with p < b exist such that p is a base-b Wieferich prime.

Original entry on oeis.org

10768, 24599, 27557, 29957, 33301, 35397, 45009, 49085, 55241, 60661, 63290, 69389, 89101, 90607, 93657, 101305, 103751, 105657, 117618, 120473, 123824, 126449, 129473, 132857, 133524, 133948, 138149, 138896, 143882, 147717, 150793, 152985, 159317, 168920
Offset: 1

Views

Author

Felix Fröhlich, May 26 2019

Keywords

Comments

Numbers n such that A255920(n) = 9.

Crossrefs

Cf. A255920.
Cf. bases b with exactly k base-b Wieferich primes less than b: A255921 (k=0), A255922 (k=1), A255923 (k=2), A255924 (k=3), A255925 (k=4), A325881 (k=5), A325882 (k=6), A325883 (k=7), A325884 (k=8), A325886 (k=10).

Programs

  • PARI
    is(n) = my(i=0); forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, i++)); i==9

A325886 Bases b where exactly ten primes p with p < b exist such that p is a base-b Wieferich prime.

Original entry on oeis.org

13834, 73837, 151325, 172324, 182973, 213615, 233009, 275786, 283877, 296449
Offset: 1

Views

Author

Felix Fröhlich, May 26 2019

Keywords

Comments

Numbers n such that A255920(n) = 10.

Crossrefs

Cf. A255920.
Cf. bases b with exactly k base-b Wieferich primes less than b: A255921 (k=0), A255922 (k=1), A255923 (k=2), A255924 (k=3), A255925 (k=4), A325881 (k=5), A325882 (k=6), A325883 (k=7), A325884 (k=8), A325885 (k=9).

Programs

  • PARI
    is(n) = my(i=0); forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, i++)); i==10
Showing 1-9 of 9 results.

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