A011608 Legendre symbol (n,127).

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 126.

Formula

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^63 (mod 127).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-126). (End)

Mathematica

JacobiSymbol[Range[0, 100], 127] (* Paolo Xausa, Nov 10 2025 *)

Prog

(PARI) a(n) = kronecker(n, 127) \\ 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: A011605 A011606 A011607 * A011609 A011610 A011611

Adjacent sequences: A011605 A011606 A011607 * A011609 A011610 A011611

Keyword

sign,mult,easy

Author

N. J. A. Sloane

Status

approved