A020231 Strong pseudoprimes to base 5.

781, 1541, 5461, 5611, 7813, 13021, 14981, 15751, 24211, 25351, 29539, 38081, 40501, 44801, 53971, 79381, 100651, 102311, 104721, 112141, 121463, 133141, 141361, 146611, 195313, 211951, 216457, 222301, 251521, 289081, 290629, 298271, 315121

Offset: 1

Author

David W. Wilson

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..715 from R. J. Mathar)
• Eric Weisstein's World of Mathematics, Strong Pseudoprime
• Index entries for sequences related to pseudoprimes

Crossrefs

Cf. A005936, A001262 (base-2 SPP), A020229 (base-3 SPP), A215568 (SPP to bases 2 & 5), A215566 (SPP to bases 3 & 5), A056915 (SPP to bases 2, 3 & 5), A074773 (SPP to bases 2, 3, 5 & 7).

Programs

Mathematica

nmax = 400000; sppQ[n_?EvenQ, ] := False; sppQ[n?PrimeQ, ] := False; sppQ[n, b_] := (s = IntegerExponent[n-1, 2]; d = (n-1)/2^s; If[ PowerMod[b, d, n] == 1, Return[True], Do[If[PowerMod[b, d*2^r, n] == n-1, Return[True]], {r, 0, s - 1}]]); A020231 = {}; n = 1; While[n < nmax, n = n+2; If[sppQ[n, 5] == True, Print[n]; AppendTo[A020231, n]]]; A020231 (* Jean-François Alcover, Oct 20 2011, after R. J. Mathar *)