A153881 1 followed by -1, -1, -1, ... .

1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -1, -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

Author

Mats Granvik, Jan 03 2009

Keywords

• sign
• easy

Comments

Dirichlet inverse of A074206.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1).

Crossrefs

If prefixed by initial 0, we get A134824.

Cf. A074206 (Dirichlet inverse).

Cf. A033879, A055615, A057427, A063524, A344587, A346234.

Programs

Magma

[1 - 2*Sign(n-1) : n in [1..100]]; // Wesley Ivan Hurt, Jun 20 2014

Maple

A153881:=n->`if`(n=1, 1, -1); seq(A153881(n), n=1..100); # Wesley Ivan Hurt, Jun 20 2014

Mathematica

Table[1 - 2 Sign[n - 1], {n, 100}] (* Wesley Ivan Hurt, Jun 20 2014 *)

PARI

a(n)=if(n>1,-1,1) \\ Charles R Greathouse IV, Sep 24 2015

Formula

G.f: x*(1-2*x)/(1-x). - Mats Granvik, Mar 09 2009, rewritten R. J. Mathar, Mar 31 2010

a(n) = (-1)^A000040(n). - Juri-Stepan Gerasimov, Sep 10 2009

G.f.: x / (1 + x / (1 - 2*x)). - Michael Somos, Apr 02 2012

From Wesley Ivan Hurt, Jun 20 2014: (Start)

a(1) = 1; a(n) = -1, n > 1.

a(n) = 1 - 2*sign(n-1) = 1 - 2*A057427(n-1).

a(n) = (-1)^sign(1-n) = (-1)^A057427(1-n).

a(n) = 2*floor(1/n)-1 = 2*A063524(n)-1. (End)

Dirichlet g.f.: 2 - zeta(s). - Álvar Ibeas, Dec 30 2018

a(n) = Sum_{d|n} A033879(d)*A055615(n/d) = Sum_{d|n} A344587(d)*A346234(n/d). - Antti Karttunen, Nov 22 2024

Extensions

Edited by Charles R Greathouse IV, Mar 18 2010

More terms from Antti Karttunen, Nov 22 2024