A011611 Legendre symbol (n,139).

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 138.

Formula

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^69 (mod 139).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-138). (End)

Mathematica

JacobiSymbol[Range[0, 100], 139] (* Paolo Xausa, Nov 10 2025 *)

Prog

(PARI) a(n) = kronecker(n, 139) \\ 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: A011608 A011609 A011610 * A011612 A011613 A011614

Adjacent sequences: A011608 A011609 A011610 * A011612 A011613 A011614

Keyword

sign,mult,easy,changed

Author

N. J. A. Sloane

Status

approved