A112347 Kronecker symbol (-1, n) except a(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

Offset: 0

Author

Michael Somos, Sep 12 2005

Keywords

• sign
• mult

Examples

			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 + ...
		

Links

• J.-P. Allouche and J. Shallit, On three conjectures of P. Barry, arxiv preprint arXiv:2006.04708 [math.NT], June 8 2020.
• Paul Barry, Some observations on the Rueppel sequence and associated Hankel determinants, arXiv:2005.04066 [math.CO], 2020.
• Index entries for sequences obtained by enumerating foldings

Crossrefs

Cf. A034947.

First differences of A005811.

Programs

Mathematica

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

PARI

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

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.