A240660 Least k such that 5^k == -1 (mod prime(n)), or 0 if no such k exists.

1, 1, 0, 3, 0, 2, 8, 0, 11, 7, 0, 18, 10, 21, 23, 26, 0, 15, 11, 0, 36, 0, 41, 22, 48, 0, 51, 53, 0, 56, 21, 0, 68, 0, 0, 0, 78, 27, 83, 86, 0, 0, 0, 96, 98, 0, 0, 111, 113, 57, 116, 0, 20, 0, 128, 131, 0, 0, 138, 70, 141, 146, 153, 0, 4, 158, 0, 56, 173, 87

Offset: 1

Author

T. D. Noe, Apr 14 2014

Keywords

• nonn

Comments

The least k, if it exists, such that prime(n) divides 5^k + 1.

Links

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

Crossrefs

Cf. A211241 (order of 5 mod prime(n)).

Programs

Mathematica

Table[p = Prime[n]; s = Select[Range[p/2], PowerMod[5, #, p] == p - 1 &, 1]; If[s == {}, 0, s[[1]]], {n, 100}]

Formula

a(1) = 1; for n > 1, a(n) = A211241(n)/2 if A211241(n) is even, otherwise 0.