A372494 - OEIS

A372494

For n >= 1, a(n) is the least k >= 0 such that k^2 + k + 1 is divisible by 2^n - 1 or a(n) = -1 if no such k exists.

0, 1, 2, -1, 5, -1, 19, -1, 81, -1, -1, -1, 90, 1885, 4799, -1, 21905, -1, 69492, -1, 99206, -1, -1, -1, 585398, 8985436, 32569980, -1, -1, -1, 634005911, -1, -1, -1, -1, -1, 7348910325, 40154162248, 28169995830, -1, -1, -1, -1, -1, 749259285289, -1, -1, -1, 22640169503650

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OFFSET

1,3

LINKS

Chai Wah Wu, Table of n, a(n) for n = 1..200

EXAMPLE

n = 5: (k^2 + k + 1) / (2^5 - 1) is true for the least k = 5, thus a(5) = 5.

n = 7: (k^2 + k + 1) / (2^7 - 1) is true for the least k = 19, thus a(7) = 19.

PROG

(Python)

from sympy import sqrt_mod_iter

def A372494(n):