A011609 Legendre symbol (n,131).

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, -1, -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

Paolo Xausa, Table of n, a(n) for n = 0..10000

Index entries for linear recurrences with constant coefficients, order 130.

Formula

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^65 (mod 131).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-130). (End)

Mathematica

JacobiSymbol[Range[0, 100], 131] (* Paolo Xausa, Nov 10 2025 *)

Prog

(PARI) a(n) = kronecker(n, 131) \\ Jianing Song, Jun 12 2026

Crossrefs

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

Sequence in context: A011606 A011607 A011608 * A011610 A011611 A011612

Adjacent sequences: A011606 A011607 A011608 * A011610 A011611 A011612

Keyword

sign,mult,easy,changed

Author

N. J. A. Sloane

Status

approved