A011613 - OEIS

%I #21 Jun 12 2026 10:10:44

%S 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,

%T -1,1,-1,1,1,-1,1,-1,1,1,1,1,1,-1,1,1,1,1,-1,1,-1,1,1,-1,-1,-1,-1,1,

%U -1,-1,1,1,-1,-1,1,-1,1,-1,-1,-1,1,1,-1,-1,1,-1,1,-1,1,-1,1,-1,1

%N Legendre symbol (n,151).

%D G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers. 3rd ed., Oxford Univ. Press, 1954, p. 68.

%H Paolo Xausa, <a href="/A011613/b011613.txt">Table of n, a(n) for n = 0..10000</a>

%H <a href="/index/Rec#order_150">Index entries for linear recurrences with constant coefficients</a>, order 150.

%F From _Jianing Song_, Jun 12 2026: (Start)

%F a(n) == n^75 (mod 151).

%F Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-150). (End)

%t JacobiSymbol[Range[0, 100], 151] (* _Paolo Xausa_, Nov 10 2025 *)

%o (PARI) a(n) = kronecker(n, 151) \\ _Jianing Song_, Jun 12 2026

%Y Legendre symbols mod p: A102283 (p=3), A080891 (p=5), A175629 (p=7), A011582-A011631 (p=11-251), A165573 (p=257), A165574 (p=263).

%K sign,mult,easy,changed

%O 0,1

%A _N. J. A. Sloane_