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

%I A255924 #12 Feb 16 2025 08:33:25
%S A255924 19,28,53,68,80,89,107,129,137,143,145,146,147,148,170,177,181,197,
%T A255924 215,224,253,263,268,299,307,324,332,333,334,339,341,349,350,354,357,
%U A255924 359,360,362,368,373,377,389,393,399,402,403,410,413,437,440,449,451,457
%N A255924 Bases b for which exactly three Wieferich primes p with p < b exist such that p is a base-b Wieferich prime.
%C A255924 Numbers b such that A255920(b) = 3.
%H A255924 Felix Fröhlich, <a href="/A255924/b255924.txt">Table of n, a(n) for n = 1..10000</a>
%H A255924 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/WieferichPrime.html">Wieferich Prime</a>
%o A255924 (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
%o A255924 (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
%Y A255924 Cf. A255920.
%Y A255924 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).
%K A255924 nonn
%O A255924 1,1
%A A255924 _Felix Fröhlich_, Mar 23 2015