A011596 Legendre symbol (n,67).

0, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1, 1, 1, 1, 1, -1, 1, -1, 1, 1, 1, 1, 1, 1, -1, -1, 1, -1, -1, -1, 1, -1, 1, 1, 1, -1, 1, 1, -1, -1, -1, -1, -1, -1, 1, -1, 1, -1, -1, -1, -1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1, 1, -1, 0, 1, -1, -1, 1, -1, 1, -1, -1, 1, 1, -1, -1, -1

Offset

0,1

References

G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 68.

Links

Andrew Howroyd, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, signature (-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1).

Formula

a(n) = a(n-67). - Andrew Howroyd, Nov 17 2025

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^33 (mod 67).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-66). (End)

Mathematica

JacobiSymbol[Range[0, 100], 67] (* Harvey P. Dale, Jan 07 2023 *)

Prog

(PARI) a(n) = kronecker(n, 67); \\ Andrew Howroyd, Nov 17 2025

Crossrefs

Moebius transform of A318982.

Cf. A106933 (primes not inert in Q(sqrt(-67))), A191041 (primes decomposing), A191077 (primes remaining inert).

Legendre symbols mod p: A102283 (p=3), A080891 (p=5), A175629 (p=7), A011582-A011631 (p=11-251), A165573 (p=257), A165574 (p=263).

Kronecker symbols {(D/n)} for negative fundamental discriminants D = -3..-47, -67, -163: A102283, A101455, A175629, A188510, A011582, A316569, A011585, A289741, A011586, A109017, A011588, A390614, A388073, A388072, A011591, A011592, this sequence, A011615.

Kronecker symbols {(D/n)} for positive fundamental discriminants D = 5..41: A080891, A091337, A110161, A011583, A011584, A322829, A322796, A390615, A011587, A391502, A011589, A391503, A011590.

Sequence in context: A011593 A011594 A011595 * A011597 A070747 A070750

Adjacent sequences: A011593 A011594 A011595 * A011597 A011598 A011599

Keyword

sign,mult,easy

Author

N. J. A. Sloane

Status

approved