A090088 - OEIS

%I #17 Mar 26 2021 06:31:41

%S 4,286,4,6,4,10,4,14,4,6,4,22,4,26,4,6,4,34,4,38,4,6,4,46,4,10,4,6,4,

%T 58,4,62,4,6,4,10,4,74,4,6,4,82,4,86,4,6,4,94,4,14,4,6,4,106,4,10,4,6,

%U 4,118,4,122,4,6,4,10,4,134,4,6,4,142,4,146,4,6,4,14,4,158,4,6,4,166,4,10

%N Smallest even pseudoprimes to odd base=2n-1, not necessarily exceeding n. See also A007535 and A090086, A090087.

%C For an even base there are no even pseudoprimes.

%H Antti Karttunen, <a href="/A090088/b090088.txt">Table of n, a(n) for n = 1..16520</a>

%H Antti Karttunen, <a href="/A090088/a090088.txt">Data supplement: n, a(n) computed for n =  1..100000</a>

%F a(n) = Min_{x=even number; (-1 + n^(x-1)) mod x = 0}.

%e n=2, 2n-2=3 as base, smallest relevant power is -1+2^(286-1) which is divisible by 286.

%t Array[Block[{k = 4}, While[PowerMod[2 # - 1, k - 1, k] != 1, k += 2]; k] &, 86] (* _Michael De Vlieger_, Nov 13 2018 *)

%o (PARI) A090088(n) = { forstep(k=4, oo, 2, if(1==(Mod(n+n-1, k)^(k-1)), return (k)); ); } \\ (After code in A090086) - _Antti Karttunen_, Nov 10 2018

%Y Cf. A007535, A090986, A090987, A090089.

%K nonn

%O 1,1

%A _Labos Elemer_, Nov 25 2003