A240663 Least k such that 8^k == -1 (mod prime(n)), or 0 if no such k exists.

0, 1, 2, 0, 5, 2, 4, 3, 0, 14, 0, 6, 10, 7, 0, 26, 29, 10, 11, 0, 0, 0, 41, 0, 8, 50, 0, 53, 6, 14, 0, 65, 34, 23, 74, 0, 26, 27, 0, 86, 89, 30, 0, 16, 98, 0, 35, 0, 113, 38, 0, 0, 4, 25, 8, 0, 134, 0, 46, 35, 47, 146, 17, 0, 26, 158, 5, 0, 173, 58, 44, 0, 0, 62

Offset: 1

Author

T. D. Noe, Apr 14 2014

Keywords

• nonn

Comments

The least k, if it exists, such that prime(n) divides 8^k + 1.

Links

• T. D. Noe, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A211244 (order of 8 mod prime(n)).

Programs

Mathematica

Table[p = Prime[n]; s = Select[Range[p/2], PowerMod[8, #, p] == p - 1 &, 1]; If[s == {}, 0, s[[1]]], {n, 100}]

Formula

a(n) = A211244(n)/2 if A211244(n) is even, otherwise 0.