A090088 Smallest even pseudoprimes to odd base=2n-1, not necessarily exceeding n. See also A007535 and A090086, A090087.

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, 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, 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

Offset: 1

Author

Labos Elemer, Nov 25 2003

Keywords

• nonn

Comments

For an even base there are no even pseudoprimes.

Examples

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

Links

• Antti Karttunen, Table of n, a(n) for n = 1..16520
• Antti Karttunen, Data supplement: n, a(n) computed for n = 1..100000

Crossrefs

Cf. A007535, A090986, A090987, A090089.

Programs

Mathematica

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

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

Formula

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