A011614 Legendre symbol (n,157).

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 156.

Formula

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^78 (mod 157).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-156). (End)

Mathematica

JacobiSymbol[Range[0, 100], 157] (* Paolo Xausa, Nov 10 2025 *)

Prog

(PARI) a(n) = kronecker(n, 157) \\ 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: A011611 A011612 A011613 * A011615 A011616 A011617

Adjacent sequences: A011611 A011612 A011613 * A011615 A011616 A011617

Keyword

sign,mult,easy

Author

N. J. A. Sloane

Status

approved