A020280 Strong pseudoprimes to base 54.

55, 341, 361, 385, 1247, 2701, 2863, 4033, 4069, 7957, 9073, 14905, 15409, 21349, 22495, 27157, 29341, 32689, 33227, 37921, 42001, 42121, 42127, 49141, 55831, 56449, 60701, 62893, 70801, 77293, 83333, 107929, 128143, 132193, 145921, 150553, 152497

Offset

1,1

Links

R. J. Mathar, Table of n, a(n) for n = 1..300

Eric Weisstein's World of Mathematics, Strong Pseudoprime

Index entries for sequences related to pseudoprimes

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[54, #] &] (* Alonso del Arte, Aug 03 2018 *)

Prog

(PARI)
oddpart(n) = if (n % 2, n, oddpart(n/2))
isA020280(n) = {local(d, s, res); d = oddpart(n - 1); s = bigomega((n - 1)/d); /* count factors of 2 */
res = 0; if(s != 0 & !isprime(n), /* n is odd and composite */
if (Mod(54, n)^d == Mod(1, n), res = 1, /* 54^d = 1 (mod n) */
for (r = 0, s - 1, if (Mod(54, n)^(d * 2^r) == Mod(-1, n), res = 1)))); res} // 54^(d * 2^r) = -1 (mod n) \\ Michael B. Porter, Oct 23 2009

Crossrefs

Sequence in context: A140197 A250841 A250834 * A063653 A222348 A075740

Adjacent sequences: A020277 A020278 A020279 * A020281 A020282 A020283

Keyword

nonn

Author

David W. Wilson

Status

approved