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A090089 Smallest even pseudoprimes to odd base=4n-1, not necessarily exceeding n.

%I A090089 #9 Nov 11 2019 04:40:10
%S A090089 286,6,10,14,6,22,26,6,34,38,6,46,10,6,58,62,6,10,74,6,82,86,6,94,14,
%T A090089 6,106,10,6,118,122,6,10,134,6,142,146,6,14,158,6,166,10,6,178,14,6,
%U A090089 10,194,6,202,206,6,214,218,6,226,10,6,14,22,6,10,254,6,262,14,6,274,278,6
%N A090089 Smallest even pseudoprimes to odd base=4n-1, not necessarily exceeding n.
%C A090089 There are no even pseudoprimes to an even base.
%H A090089 Amiram Eldar, <a href="/A090089/b090089.txt">Table of n, a(n) for n = 1..10000</a>
%F A090089 a(n)=Min{x=4n-1 number; Mod[ -1+n^(x-1), x]=0}
%e A090089 n=1: base = 4n-1=3, smallest relevant power is -1+2^(286-1) which is divisible by 286.
%e A090089 Sieving further residue classes, smallest regularly arising pseudoprimes are 6,10 etc..
%t A090089 a[n_] := Module[{k = 2}, While[GCD[n, k] > 1 || PrimeQ[k] || PowerMod[n, k - 1, k] != 1, k += 2]; k]; Table[a[4*n - 1], {n, 1, 100}] (* _Amiram Eldar_, Nov 11 2019 *)
%Y A090089 Cf. A007535, A090085, A090986, A090087, A090088.
%K A090089 nonn
%O A090089 1,1
%A A090089 _Labos Elemer_, Nov 25 2003