cp's OEIS Frontend

A112347 Kronecker symbol (-1, n) except a(0) = 0.

%I A112347 #25 Jun 27 2022 21:24:10
%S A112347 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 A112347 -1,1,-1,-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 A112347 -1,-1,1,1,-1,-1,1,-1,-1,1,1,1,-1,1,1,-1,-1,1,1,1,-1,-1,1,-1,-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 A112347 Kronecker symbol (-1, n) except a(0) = 0.
%H A112347 J.-P. Allouche and J. Shallit, <a href="https://arxiv.org/abs/2006.04708">On three conjectures of P. Barry</a>, arxiv preprint arXiv:2006.04708 [math.NT], June 8 2020.
%H A112347 Paul Barry, <a href="https://arxiv.org/abs/2005.04066">Some observations on the Rueppel sequence and associated Hankel determinants</a>, arXiv:2005.04066 [math.CO], 2020.
%H A112347 <a href="/index/Fo#fold">Index entries for sequences obtained by enumerating foldings</a>
%F A112347 Multiplicative with a(2^e) = 1, a(p^e) = (-1)^(e(p-1)/2) if p>2.
%F A112347 a(2n) = a(n), a(4*n + 1) = 1, a(4*n + 3) = -1. a(-n) = -a(n).
%F A112347 a(n) = A034947(n) unless n=0.
%e A112347 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 + ...
%t A112347 Join[{0},KroneckerSymbol[-1,Range[110]]] (* _Harvey P. Dale_, Jun 02 2019 *)
%o A112347 (PARI) {a(n) = if( n, kronecker( -1, n))}
%Y A112347 Cf. A034947.
%Y A112347 First differences of A005811.
%K A112347 sign,mult
%O A112347 0,1
%A A112347 _Michael Somos_, Sep 12 2005