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

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

1,1

Comments

Numbers b such that A255920(b) = 4.

Links

Felix Fröhlich, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Wieferich Prime

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 *)

Prog

(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

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).

Sequence in context: A051116 A381797 A327110 * A095623 A257197 A105934

Adjacent sequences: A255922 A255923 A255924 * A255926 A255927 A255928

Keyword

nonn

Author

Felix Fröhlich, Mar 23 2015

Status

approved