A011598 Legendre symbol (n,73).

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, 0, 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).

Formula

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^36 (mod 73).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-72). (End)

Mathematica

JacobiSymbol[Range[0, 100], 73] (* Paolo Xausa, Nov 09 2025 *)

Prog

(PARI) a(n) = kronecker(n, 73) \\ Jianing Song, Jun 12 2026

Crossrefs

Cf. A038957 (primes not inert in Q(sqrt(73))), A191045 (primes decomposing), A038958 (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: A011597 A070747 A070750 * A324672 A330035 A011599

Adjacent sequences: A011595 A011596 A011597 * A011599 A011600 A011601

Keyword

sign,mult,easy,changed

Author

N. J. A. Sloane

Status

approved