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

1,1

Comments

For an even base there are no even pseudoprimes.

Links

Antti Karttunen, Table of n, a(n) for n = 1..16520

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A007535, A090986, A090987, A090089.

Sequence in context: A074309 A113256 A259495 * A253233 A242997 A221135

Adjacent sequences: A090085 A090086 A090087 * A090089 A090090 A090091

Keyword

nonn

Author

Labos Elemer, Nov 25 2003

Status

approved