A020229 Strong pseudoprimes to base 3.

121, 703, 1891, 3281, 8401, 8911, 10585, 12403, 16531, 18721, 19345, 23521, 31621, 44287, 47197, 55969, 63139, 74593, 79003, 82513, 87913, 88573, 97567, 105163, 111361, 112141, 148417, 152551, 182527, 188191, 211411, 218791, 221761, 226801

Offset

1,1

Links

Charles R Greathouse IV, Table of n, a(n) for n = 1..24767 (first 752 terms from R. J. Mathar)

Joerg Arndt, Matters Computational (The Fxtbook), section 39.10, pp. 786-792

Eric Weisstein's World of Mathematics, Strong Pseudoprime

Index entries for sequences related to pseudoprimes

Mathematica

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}]]); A020229 = {}; lst = {}; k = 3; While[k < 500000, If[sppQ[k, 3], Print[k]; AppendTo[lst, k]]; k += 2]; lst (* Jean-François Alcover, Oct 20 2011, after R. J. Mathar *)

Prog

(PARI) is_A020229(n, b=3)={ bittest(n, 0) || return; ispseudoprime(n) && return; my(d=(n-1)>>valuation(n-1, 2)); Mod(b, n)^d==1 || until(n-1<=d*=2, Mod(b, n)^d+1 || return(1))} \\ M. F. Hasler, Jul 19 2012

Crossrefs

Cf. A001262, A072276, A056915, A074773, A005935.

Sequence in context: A262051 A048950 A329705 * A141350 A235408 A361703

Adjacent sequences: A020226 A020227 A020228 * A020230 A020231 A020232

Keyword

nonn

Author

David W. Wilson

Status

approved