A011623 Legendre symbol (n,199).

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 198.

Formula

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^99 (mod 199).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-198). (End)

Mathematica

JacobiSymbol[Range[0, 100], 199] (* Paolo Xausa, Nov 10 2025 *)

Prog

(PARI) a(n) = kronecker(n, 199) \\ 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: A011620 A011621 A011622 * A011624 A011625 A011626

Adjacent sequences: A011620 A011621 A011622 * A011624 A011625 A011626

Keyword

sign,mult,easy,changed

Author

N. J. A. Sloane

Status

approved