A240659 Least k such that 4^k == -1 (mod prime(n)), or 0 if no such k exists.

0, 0, 1, 0, 0, 3, 2, 0, 0, 7, 0, 9, 5, 0, 0, 13, 0, 15, 0, 0, 0, 0, 0, 0, 12, 25, 0, 0, 9, 7, 0, 0, 17, 0, 37, 0, 13, 0, 0, 43, 0, 45, 0, 24, 49, 0, 0, 0, 0, 19, 0, 0, 6, 0, 4, 0, 67, 0, 23, 0, 0, 73, 0, 0, 39, 79, 0, 0, 0, 87, 22, 0, 0, 93, 0, 0, 97, 11, 50, 51

Offset: 1

Author

T. D. Noe, Apr 14 2014

Keywords

• nonn

Comments

The least k, if it exists, such that prime(n) divides 4^k + 1.

Links

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

Crossrefs

Cf. A082654 (order of 4 mod prime(n)).

Programs

Mathematica

Table[p = Prime[n]; s = Select[Range[p/2], PowerMod[4, #, p] == p - 1 &, 1]; If[s == {}, 0, s[[1]]], {n, 100}]

Formula

a(n) = A082654(n)/2 if A082654(n) is even, otherwise 0.