A240666 Least k such that k^m == -1 (mod prime(n)) has a solution for some m.

3, 2, 2, 3, 2, 2, 2, 2, 5, 2, 3, 2, 2, 2, 5, 2, 2, 2, 2, 7, 3, 3, 2, 3, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 2, 2, 5, 2, 2, 2, 7, 2, 2, 3, 2, 3, 2, 2, 3, 7, 2, 2, 2, 5, 2, 3, 2, 2, 2, 2, 2, 11, 2, 2, 2, 3, 2, 2, 2, 7, 3, 2, 2, 5, 2, 2, 2, 2, 2, 2, 7, 2, 3, 2, 2

Offset: 1

Author

T. D. Noe, Apr 15 2014

Keywords

• nonn

Comments

Looking at sequences A240657-A240665, one sees many 0 terms. This sequence finds the least k having a solution. Is the least k always prime?

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A240657-A240665.

Programs

Mathematica

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