Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #44 Feb 07 2018 17:19:44
%S 121,703,1891,3281,8401,8911,10585,12403,16531,18721,19345,23521,
%T 31621,44287,47197,55969,63139,74593,79003,82513,87913,88573,97567,
%U 105163,111361,112141,148417,152551,182527,188191,211411,218791,221761,226801
%N Strong pseudoprimes to base 3.
%H Charles R Greathouse IV, <a href="/A020229/b020229.txt">Table of n, a(n) for n = 1..24767</a> (first 752 terms from R. J. Mathar)
%H Joerg Arndt, <a href="http://www.jjj.de/fxt/#fxtbook">Matters Computational (The Fxtbook)</a>, section 39.10, pp. 786-792
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/StrongPseudoprime.html">Strong Pseudoprime</a>
%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>
%t 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_ *)
%o (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
%Y Cf. A001262, A072276, A056915, A074773, A005935.
%K nonn
%O 1,1
%A _David W. Wilson_