A112347 - OEIS

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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 (list; graph; refs; listen; history; text; internal format)

	OFFSET	`0,1`
	LINKS	`Table of n, a(n) for n=0..102.` `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`
	FORMULA	`Multiplicative with a(2^e) = 1, a(p^e) = (-1)^(e(p-1)/2) if p>2.` `a(2n) = a(n), a(4n + 1) = 1, a(4n + 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.` `First differences of A005811.` `Sequence in context: A070238 A062157 A103131 * A057427 A178334 A000007` `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 August 18 08:16 EDT 2024. Contains 375255 sequences. (Running on oeis4.)