A261012 Sign(n) (with offset -1): a(n) = 1 if n>0, = -1 if n<0, = 0 if n = 0.

-1, 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, 1, 1

Offset

-1,1

Comments

For nonnegative n, partial sums of A063524 (characteristic function of 1). - Jeremy Gardiner, Sep 08 2002

For nonnegative n, characteristic function of positive integers. - Franklin T. Adams-Watters, Aug 01 2011

a(A000027(n)) = 1; a(A000004(n)) = 0. - Reinhard Zumkeller, Oct 11 2008

Central terms of the triangle in A152487. - Reinhard Zumkeller, Dec 06 2008

n-th prime mod 2 (with offset 1,1). - Philippe Deléham, Apr 04 2009

References

T. M. Macrobert, Functions of a Complex Variable, 4th ed., Macmillan and Co, London, 1958, p. 90

Links

Table of n, a(n) for n=-1..104.

Index entries for characteristic functions

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

Formula

G.f.: Sum_{k>=0} 2^k*x^(2^k)/(1+x^(2^k)). - Michael Somos, Sep 11 2005

For n>=0, a(n) = A000007(0^n). - Jaume Oliver Lafont, Mar 19 2009

a(0) = 0, a(n) = n/|n| or |n|/n for n != 0. - Jon Perry, Sep 20 2012

G.f.: -(x^2+x-1) / (x*(x-1)). - Colin Barker, Mar 13 2014

Maple

with(numtheory); A057427:=n->signum(n); seq(A057427(k), k=-1..50); # Wesley Ivan Hurt, Oct 22 2013

Mathematica

Sign[Range[-1, 120]] (* or *) PadRight[{-1, 0}, 120, {1}] (* Harvey P. Dale, May 12 2019 *)

Prog

(PARI) a(n)=sign(n)
(Haskell)
a261012 = signum
a261012_list = -1 : 0 : [1, 1 ..] -- Reinhard Zumkeller, Nov 28 2012

Crossrefs

A057427 is the official entry for sign(n) or signum(n). - N. J. A. Sloane, Aug 16 2015

Sequence in context: A105812 A134323 A060576 * A019590 A154955 A240356

Adjacent sequences: A261009 A261010 A261011 * A261013 A261014 A261015

Keyword

easy,sign,mult

Author

Henry Bottomley, Sep 05 2000

Extensions

a(-1) = -1 added by Jon Perry, Sep 20 2012

Incorrect g.f. and e.g.f. removed by Joerg Arndt, Oct 22 2013

The initial a(-1)=-1 should never have been added.

Status

approved