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.

Previous Showing 11-13 of 13 results.

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

A273786 Numbers n where a prime p < n exists such that n^(p-1) == 1 (mod p^2), i.e., such that p is a base-n Wieferich prime.

Original entry on oeis.org

5, 7, 8, 9, 10, 13, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 35, 37, 38, 40, 41, 42, 43, 44, 45, 46, 48, 49, 50, 51, 53, 54, 55, 57, 60, 61, 62, 63, 64, 65, 67, 68, 69, 70, 71, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 85, 89, 91, 93, 94
Offset: 1

Views

Author

Felix Fröhlich, May 30 2016

Keywords

Comments

Numbers n such that A255920(n) > 0.
Complement of A255921. - Felix Fröhlich, Dec 03 2020

Examples

			The prime 5 satisfies 24^(5-1) == 1 (mod 5^2) and 5 < 24, so 24 is a term of the sequence.

Links

Crossrefs

Cf. A255920, A255921, A273785.

Programs

  • Mathematica
    Select[Range@ 94, Function[n, Count[Prime@ Range@ PrimePi@ n, p_ /; Mod[n^(p - 1), p^2] == 1] > 0]] (* Michael De Vlieger, May 30 2016 *)
  • PARI
    is(n) = forprime(p=1, n-1, if(Mod(n, p^2)^(p-1)==1, return(1))); 0

A284044 Largest positive k among all primes p < n such that n^(p-1) == 1 (mod p^k).

Original entry on oeis.org

1, 1, 2, 1, 2, 2, 3, 2, 1, 1, 2, 1, 1, 1, 4, 3, 3, 1, 2, 2, 2, 2, 3, 3, 2, 3, 2, 2, 2, 2, 5, 1, 2, 1, 2, 2, 1, 2, 3, 3, 2, 2, 2, 2, 1, 2, 4, 2, 2, 1, 3, 2, 3, 1, 3, 1, 1, 2, 2, 2, 2, 2, 6, 1, 2, 3, 2, 2, 2, 1, 3, 2, 2, 2, 2, 2, 2, 4, 4, 4, 1, 1, 2, 1, 1, 1, 3
Offset: 3

Views

Author

Felix Fröhlich, Apr 02 2017

Keywords

Comments

a(n) > 1 iff A255920(n) > 0, i.e., iff n is a term of A273786.

Examples

			For n = 7: the maximal exponents k in the congruence 7^(p-1) == 1 (mod p^k) for p = 2, 3, 5 are 1, 1, 2, respectively. Since 2 is the largest exponent among that list, a(7) = 2.

Crossrefs

Cf. A255920, A258045, A268310, A273786, A278701, A282902.

Programs

  • PARI
    a(n) = my(r=1); forprime(p=1, n-1, my(k=1); while(1, if(Mod(n, p^k)^(p-1)!=1, k--; break, k++)); if(k > r, r=k)); r
Previous Showing 11-13 of 13 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement.