A165476 Legendre symbol (n,131071).

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, 1, -1, 1, -1, 1

Offset

0,1

Comments

131071 is the 6th Mersenne prime, A000668(6).

See row 12251 in triangle A226520, A000040(12251) = 131071. - Reinhard Zumkeller, Feb 02 2014

Links

A. Karttunen, Table of n, a(n) for n = 0..131071

Wikipedia, Legendre symbol.

Index entries for periodic sequences.

Index entries for linear recurrences with constant coefficients, order 131070.

Formula

From Jianing Song, Jun 12 2026: (Start)

a(n) == n^65535 (mod 131071).

Recurrence: a(n) = -a(n-1) - a(n-2) - .... - a(n-131070). (End)

Mathematica

a[n_] := JacobiSymbol[n, 2^17 - 1];
Table[a[n], {n, 0, 100}] (* Jean-François Alcover, Jan 13 2023 *)

Prog

(Haskell)
a165476 = flip legendreSymbol 131071
-- Where the function legendreSymbol is defined in A097343.
-- Reinhard Zumkeller, Feb 02 2014
(PARI) a(n)=kronecker(n, 131071) \\ Charles R Greathouse IV, May 26 2026

Crossrefs

Partial sums: A165477.

Cf. A097343, A165471, A165581, A165591, A165596, A000668, A226520, A000040.

Sequence in context: A165581 A165586 A134824 * A165596 A226523 A070238

Adjacent sequences: A165473 A165474 A165475 * A165477 A165478 A165479

Keyword

sign,mult,easy

Author

Antti Karttunen, Sep 21 2009

Status

approved