A240665 Least k such that 10^k == -1 (mod prime(n)), or 0 if no such k exists.

0, 0, 0, 3, 1, 3, 8, 9, 11, 14, 0, 0, 0, 0, 23, 0, 29, 30, 0, 0, 4, 0, 0, 22, 48, 2, 17, 0, 54, 56, 21, 65, 4, 23, 74, 0, 39, 0, 83, 0, 89, 90, 0, 96, 49, 0, 15, 111, 0, 114, 116, 0, 15, 25, 128, 131, 134, 0, 0, 14, 0, 73, 0, 0, 156, 0, 55, 168, 0, 58, 16, 0

Offset: 1

Author

T. D. Noe, Apr 14 2014

Keywords

• nonn

Comments

The least k, if it exists, such that prime(n) divides 10^k + 1.

Links

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

Crossrefs

Cf. A002371 (order of 10 mod prime(n)), A068958.

Programs

Mathematica

Table[p = Prime[n]; s = Select[Range[p/2], PowerMod[10, #, p] == p - 1 &, 1]; If[s == {}, 0, s[[1]]], {n, 100}]

Formula

a(n) = A002371(n)/2 if A002371(n) is even, otherwise 0.

a(n) = A068958(n) for n > 3. - Georg Fischer, Oct 23 2018