A011610 Legendre symbol (n,137).

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 136.

Formula

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^68 (mod 137).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-136). (End)

Mathematica

JacobiSymbol[Range[0, 100], 137] (* Paolo Xausa, Nov 10 2025 *)

Prog

(PARI) a(n) = kronecker(n, 137) \\ 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: A011607 A011608 A011609 * A011611 A011612 A011613

Adjacent sequences: A011607 A011608 A011609 * A011611 A011612 A011613

Keyword

sign,mult,easy,changed

Author

N. J. A. Sloane

Status

approved