A240657 Least k such that 2^k == -1 (mod prime(n)), or 0 if no such k exists.

0, 1, 2, 0, 5, 6, 4, 9, 0, 14, 0, 18, 10, 7, 0, 26, 29, 30, 33, 0, 0, 0, 41, 0, 24, 50, 0, 53, 18, 14, 0, 65, 34, 69, 74, 0, 26, 81, 0, 86, 89, 90, 0, 48, 98, 0, 105, 0, 113, 38, 0, 0, 12, 25, 8, 0, 134, 0, 46, 35, 47, 146, 51, 0, 78, 158, 15, 0, 173, 174, 44, 0

Offset: 1

Author

T. D. Noe, Apr 14 2014

Keywords

• nonn

Comments

The least k, if it exists, such that prime(n) divides 2^k + 1.

Links

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

Crossrefs

Cf. A014664 (order of 2 mod prime(n)), A072936 (zero terms).

Programs

Mathematica

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

Formula

a(n) = A014664(n)/2 if A014664(n) is even, otherwise 0.