A011615 Legendre symbol (n,163).

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 162.

Formula

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^81 (mod 163).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-162). (End)

Mathematica

JacobiSymbol[Range[0, 100], 163] (* Paolo Xausa, Nov 10 2025 *)

Prog

(PARI) a(n) = kronecker(n, 163) \\ Jianing Song, Jun 12 2026

Crossrefs

Moebius transform of A318983.

Cf. A257362 (primes not inert in Q(sqrt(-163))), A296921 (primes decomposing), A296915 (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).

Kronecker symbols {(D/n)} for negative fundamental discriminants D = -3..-47, -67, -163: A102283, A101455, A175629, A188510, A011582, A316569, A011585, A289741, A011586, A109017, A011588, A390614, A388073, A388072, A011591, A011592, A011596, this sequence.

Kronecker symbols {(D/n)} for positive fundamental discriminants D = 5..41: A080891, A091337, A110161, A011583, A011584, A322829, A322796, A390615, A011587, A391502, A011589, A391503, A011590.

Sequence in context: A011612 A011613 A011614 * A011616 A011617 A011618

Adjacent sequences: A011612 A011613 A011614 * A011616 A011617 A011618

Keyword

sign,mult,easy,changed

Author

N. J. A. Sloane

Status

approved