A165574 -id:A165574 - cp's OEIS frontend

A165576 Partial sums of A165574.

0, 1, 2, 3, 4, 3, 4, 3, 4, 5, 4, 5, 6, 7, 6, 5, 6, 7, 8, 7, 6, 5, 6, 7, 8, 9, 10, 11, 10, 9, 8, 9, 10, 11, 12, 13, 14, 15, 14, 15, 14, 13, 12, 13, 14, 13, 14, 13, 14, 15, 16, 17, 18, 17, 18, 17, 16, 15, 14, 13, 12, 13, 14, 13, 14, 13, 14, 13, 14, 15, 16, 15, 16, 15, 16, 17, 16, 15

Offset: 0

Antti Karttunen, Sep 22 2009

nonn

Period 263. There are no negative values as 263 is one of the primes in A095102.

A. Karttunen, Table of n, a(n) for n = 0..59701

Similar sequences: A165575-A165579, A165472, A165477, A165482, A165582, A165587, A165592, A165597.

Accumulate[JacobiSymbol[Range[0,90],263]] (* Harvey P. Dale, Sep 01 2021 *)

A175629 Legendre symbol (n,7).

Original entry on oeis.org

0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1, -1, 1, -1, -1, 0, 1, 1

Offset: 0

R. J. Mathar, Jul 29 2010

This represents a non-principal Dirichlet character modulo 7.

T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1986, page 139, k=7, Chi_2(n).

Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1,-1,-1).

Cf. A089509, A097343.
The Legendre symbols (n,p): A091337 (p = 2, Kronecker symbol), A102283 (p = 3), A080891 (p = 5), this sequence (p = 7), A011582 (p = 11), A011583 (p = 13), ..., A011631 (p = 251), A165573 (p = 257), A165574 (p = 263). Also, many other sequences for p > 263 are in the OEIS.
Moebius transform of A035182.

&cat [[0, 1, 1, -1, 1, -1, -1]^^20]; // Vincenzo Librandi, Jun 30 2018

A := proc(n) numtheory[jacobi](n,7) ; end proc: seq(A(n),n=0..120) ;

LinearRecurrence[{-1,-1,-1,-1,-1,-1},{0,1,1,-1,1,-1},100] (* or *) PadRight[ {},100,{0,1,1,-1,1,-1,-1}] (* Harvey P. Dale, Aug 02 2013 *)
Table[JacobiSymbol[n, 7], {n, 0, 100}] (* Vincenzo Librandi, Jun 30 2018 *)

a(n) = kronecker(n, 7); \\ Michel Marcus, Jan 28 2019

a(n) = a(n+7).
|a(n)| = A109720(n).
a(n) = -a(n-1) - a(n-2) - a(n-3) - a(n-4) - a(n-5) - a(n-6).
G.f.: x*(1 + 2*x + x^2 + 2*x^3 + x^4)/(1 + x + x^2 + x^3 + x^4 + x^5 + x^6).
a(n) == n^3 (mod 7). - Jianing Song, Jun 29 2018

A165591 Jacobi symbol (n,59701).

Original entry on oeis.org

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

Antti Karttunen, Sep 22 2009

Semiprime 59701 = 227*263 = A005385(11)*A005385(12).

A. Karttunen, Table of n, a(n) for n = 0..59701

a(n) = A011626(n)*A165574(n). Partial sums: A165592. Cf. A165471.

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A165576 Partial sums of A165574.

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A175629 Legendre symbol (n,7).

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A165591 Jacobi symbol (n,59701).

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