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A112347 Kronecker symbol (-1, n) except a(0) = 0. 0
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, -1, -1, -1, 1, 1, -1, -1, 1, -1, -1, -1, 1, 1, -1, 1, 1, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..102.

FORMULA

Multiplicative with a(2^e) = 1, a(p^e) = (-1)^(e(p-1)/2) if p>2.

a(2n) = a(n), a(4*n + 1) = 1, a(4*n + 3) = -1. a(-n) = -a(n).

a(n) = A034947(n) unless n=0.

EXAMPLE

x + x^2 - x^3 + x^4 + x^5 - x^6 - x^7 + x^8 + x^9 + x^10 - x^11 - x^12 + x^13 + ...

MATHEMATICA

Join[{0}, KroneckerSymbol[-1, Range[110]]] (* Harvey P. Dale, Jun 02 2019 *)

PROG

(PARI) {a(n) = if( n, kronecker( -1, n))}

CROSSREFS

Cf. A034947.

Sequence in context: A070238 A062157 A103131 * A057427 A178334 A185016

Adjacent sequences:  A112344 A112345 A112346 * A112348 A112349 A112350

KEYWORD

sign,mult

AUTHOR

Michael Somos, Sep 12 2005

STATUS

approved

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Last modified March 28 07:59 EDT 2020. Contains 333079 sequences. (Running on oeis4.)