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Pseudoprimes to base 34.
1

%I #22 Feb 18 2020 00:28:06

%S 15,21,33,35,55,65,77,105,165,231,273,385,429,435,445,671,703,1001,

%T 1045,1065,1155,1157,1281,1365,1729,1869,1891,2035,2059,2071,2145,

%U 2779,2821,2937,3201,3605,4033,4795,5005,5161,5565,5785,5995,6305,6533,6601,6853

%N Pseudoprimes to base 34.

%C Composite numbers n such that 34^(n-1) == 1 (mod n). - _Michel Lagneau_, Feb 18 2012

%H T. D. Noe, <a href="/A020162/b020162.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Ps#pseudoprimes">Index entries for sequences related to pseudoprimes</a>

%t base = 34; b34Pseudos = {}; n = 1; While[Length[b34Pseudos] < 100, n++; If[!PrimeQ[n] && PowerMod[base, n - 1, n] == 1, AppendTo[b34Pseudos, n]]]; b34Pseudos (* _T. D. Noe_, Feb 21 2012 *)

%t searchMax = 7000; Complement[Select[Range[searchMax], PowerMod[34, # - 1, #] == 1 &], Prime[Range[PrimePi[searchMax]]]] (* _Alonso del Arte_, Feb 17 2020 *)

%Y Cf. A001567 (pseudoprimes to base 2).

%K nonn

%O 1,1

%A _David W. Wilson_