A020250 Strong pseudoprimes to base 24.

25, 175, 553, 949, 1541, 1975, 2701, 4537, 6931, 7501, 13825, 21349, 25273, 25477, 29341, 38323, 42121, 42127, 47617, 49141, 52417, 63701, 80137, 83333, 85609, 94753, 105121, 113527, 128143, 144841, 167869, 169027, 179521, 181351, 197209, 201373

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• R. J. Mathar, Table of n, a(n) for n = 1..203
• Index entries for sequences related to pseudoprimes

Programs

Mathematica

strongPseudoprimeQ[b_, n_] := Module[{rems = Table[PowerMod[b, (n - 1)/2^expo, n], {expo, 0, IntegerExponent[n - 1, 2]}]}, (rems[[-1]] == 1 || MemberQ[rems, n - 1]) && PowerMod[b, n - 1, n] == 1]; max = 5000; Select[Complement[Range[2, max], Prime[Range[PrimePi[max]]]], strongPseudoprimeQ[24, #] &] (* Alonso del Arte, Aug 03 2018 *)

PARI

is(n, a=24)= (bittest(n, 0) && !isprime(n) && n>8) || return; my(s=valuation(n-1, 2)); if(1==a=Mod(a, n)^(n>>s), return(1)); while(a!=-1 && s--, a=a^2); a==-1 \\ Felix Fröhlich, Aug 03 2018, adapted from code by M. F. Hasler in A001262