A011625 Legendre symbol (n,223).

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 222.

Formula

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^111 (mod 223).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-222). (End)

Mathematica

JacobiSymbol[Range[0, 100], 223] (* Paolo Xausa, Nov 11 2025 *)

Prog

(PARI) a(n) = kronecker(n, 223) \\ 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: A011622 A011623 A011624 * A011626 A011627 A011628

Adjacent sequences: A011622 A011623 A011624 * A011626 A011627 A011628

Keyword

sign,mult,easy

Author

N. J. A. Sloane

Status

approved