cp's OEIS Frontend

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

%I A153881 #51 Nov 22 2024 20:32:31
%S A153881 1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
%T A153881 -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,
%U A153881 -1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-1,-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 A153881 1 followed by -1, -1, -1, ... .
%C A153881 Dirichlet inverse of A074206.
%H A153881 Antti Karttunen, <a href="/A153881/b153881.txt">Table of n, a(n) for n = 1..10000</a>
%H A153881 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).
%F A153881 G.f: x*(1-2*x)/(1-x). - _Mats Granvik_, Mar 09 2009, rewritten _R. J. Mathar_, Mar 31 2010
%F A153881 a(n) = (-1)^A000040(n). - _Juri-Stepan Gerasimov_, Sep 10 2009
%F A153881 G.f.: x / (1 + x / (1 - 2*x)). - _Michael Somos_, Apr 02 2012
%F A153881 From _Wesley Ivan Hurt_, Jun 20 2014: (Start)
%F A153881 a(1) = 1; a(n) = -1, n > 1.
%F A153881 a(n) = 1 - 2*sign(n-1) = 1 - 2*A057427(n-1).
%F A153881 a(n) = (-1)^sign(1-n) = (-1)^A057427(1-n).
%F A153881 a(n) = 2*floor(1/n)-1 = 2*A063524(n)-1. (End)
%F A153881 Dirichlet g.f.: 2 - zeta(s). - _Álvar Ibeas_, Dec 30 2018
%F A153881 a(n) = Sum_{d|n} A033879(d)*A055615(n/d) = Sum_{d|n} A344587(d)*A346234(n/d). - _Antti Karttunen_, Nov 22 2024
%p A153881 A153881:=n->`if`(n=1, 1, -1); seq(A153881(n), n=1..100); # _Wesley Ivan Hurt_, Jun 20 2014
%t A153881 Table[1 - 2 Sign[n - 1], {n, 100}] (* _Wesley Ivan Hurt_, Jun 20 2014 *)
%o A153881 (Magma) [1 - 2*Sign(n-1) : n in [1..100]]; // _Wesley Ivan Hurt_, Jun 20 2014
%o A153881 (PARI) a(n)=if(n>1,-1,1) \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A153881 If prefixed by initial 0, we get A134824.
%Y A153881 Cf. A074206 (Dirichlet inverse).
%Y A153881 Cf. A033879, A055615, A057427, A063524, A344587, A346234.
%K A153881 sign,easy
%O A153881 1,1
%A A153881 _Mats Granvik_, Jan 03 2009
%E A153881 Edited by _Charles R Greathouse IV_, Mar 18 2010
%E A153881 More terms from _Antti Karttunen_, Nov 22 2024