A011617 Legendre symbol (n,173).

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 172.

Formula

Recurrence relation is a(n) = -a(n-1) - a(n-2) - ... - a(n-171) - a(n-172) for n >= 172. - Charles R Greathouse IV, Oct 01 2019

a(n) == n^86 (mod 173). - Jianing Song, Jun 12 2026

Mathematica

JacobiSymbol[Range[0, 100], 173] (* Paolo Xausa, Nov 10 2025 *)

Prog

(PARI) a(n)=kronecker(n, 173) \\ Charles R Greathouse IV, Oct 01 2019

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: A011614 A011615 A011616 * A011618 A011619 A011620

Adjacent sequences: A011614 A011615 A011616 * A011618 A011619 A011620

Keyword

sign,mult,easy,changed

Author

N. J. A. Sloane

Status

approved