A011631 Legendre symbol (n,251).

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 250.

Formula

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^125 (mod 251).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-250). (End)

Mathematica

JacobiSymbol[Range[0, 100], 251] (* Paolo Xausa, Nov 11 2025 *)

Prog

(PARI) a(n) = kronecker(n, 251) \\ Jianing Song, Jun 12 2026

Crossrefs

Legendre symbols mod p: A102283 (p=3), A080891 (p=5), A175629 (p=7), A011582-A011630 (p=11-241), this sequence (p=251), A165573 (p=257), A165574 (p=263).

Sequence in context: A011628 A011629 A011630 * A165591 A165471 A165481

Adjacent sequences: A011628 A011629 A011630 * A011632 A011633 A011634

Keyword

sign,mult,easy,changed

Author

N. J. A. Sloane

Status

approved