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A020229 Strong pseudoprimes to base 3. 17

%I

%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-Fran├žois 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_

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Last modified August 26 05:23 EDT 2019. Contains 326328 sequences. (Running on oeis4.)