A011602 Legendre symbol (n,97).

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, signature (-1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1).

Formula

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^48 (mod 97).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-96). (End)

Mathematica

JacobiSymbol[Range[0, 100], 97] (* Paolo Xausa, Nov 09 2025 *)

Prog

(PARI) a(n) = kronecker(n, 97) \\ Jianing Song, Jun 12 2026

Crossrefs

Cf. A038987 (primes not inert in Q(sqrt(97))), A191058 (primes decomposing), A038988 (primes remaining inert).

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: A011599 A011600 A011601 * A011603 A011604 A011605

Adjacent sequences: A011599 A011600 A011601 * A011603 A011604 A011605

Keyword

sign,mult,easy

Author

N. J. A. Sloane

Status

approved