A294646 - OEIS

A294646

a(n) = (1/2)^(2*n) mod (2*n+1).

1, 1, 1, 7, 1, 1, 4, 1, 1, 16, 1, 11, 25, 1, 1, 25, 4, 1, 10, 1, 1, 16, 1, 36, 13, 1, 9, 43, 1, 1, 16, 61, 1, 52, 1, 1, 64, 60, 1, 79, 1, 16, 22, 1, 64, 70, 44, 1, 70, 1, 1, 16, 1, 1, 28, 1, 59, 16, 4, 67, 31, 11, 1, 97, 1, 106, 79, 1, 1, 106, 69, 136, 100, 1, 1, 52, 64, 1, 40, 32, 1, 31, 1, 131, 169

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OFFSET

1,4

COMMENTS

a(n) is the smallest k > 0 such that k*2^(2*n) == 1 (mod 2*n+1).

a(n)*A177023(n) == 1 (mod 2*n+1).

a(n)=1 iff 2*n+1 is in A015919.

1 <= a(n) <= 2*n, and is always coprime to 2*n+1.

Conjecture: a(n) is never 2 or 2*n or 2*n-2.

a(n) = 2*n-1 iff 2*n+1 is in A006521.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000