Search: id:A057427
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%I A057427
%S A057427 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,
%T A057427 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,
%U A057427 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1
%N A057427 Sign(n): a(n) = 1 if n>0, = -1 if n<0, = 0 if n = 0.
%C A057427 For nonnegative n, partial sums of A063524 (characteristic function of 
               1). - Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Sep 08 
               2002
%C A057427 Number of binary bracelets of n beads, 0 of them 0. Number of binary 
               bracelets of n beads, 1 of them 0. Number of binary bracelets of 
               n beads, 0 of them 0, with 00 prohibited. For n>=2, a(n-1) is the 
               number of binary bracelets of n beads, one of them 0, with 00 prohibited. 
               [From Washington Bomfim (webonfim(AT)bol.com.br), Aug 27 2008]
%C A057427 a(A000027(n)) = 1; a(A000004(n)) = 0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 11 2008]
%C A057427 Central terms of the triangle in A152487. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Dec 06 2008]
%C A057427 n-th prime mod 2 (with offset 1,1). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Apr 04 2009]
%C A057427 (1-(-1)^nth prime)/2. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 25 2009]
%D A057427 T. M. Macrobert, Functions of a Complex Variable, 4th ed., Macmillan 
               and Co, London, 1958, p. 90
%H A057427 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A057427 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a>
%F A057427 G.f.: x/(1-x).
%F A057427 Alternative g.f.: sum(k>=0, t/(1-t^2), t=x^2^k) = 1/(1-x) * sum(k>=0, 
               t-t^2, t=x^2^k) = 1/(1-x)^2 * sum(k>=0, t-2t^2+t^4, t=x^2^k) 2p-1 
               (from Ralf Stephan)
%F A057427 G.f.: Sum_{k>=0} 2^k x^(2^k)/(1+x^(2^k)). - Michael Somos Sep 11 2005
%F A057427 a(n)=(1-(-1)^A000040(n))/2. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), 
               Oct 25 2009]
%o A057427 (PARI) a(n)=sign(n)
%o A057427 (PARI) /* n>=0 */ a(n)=!!n [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               Mar 19 2009]
%Y A057427 Cf. A000007. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               Mar 19 2009]
%Y A057427 Cf. A000040. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 
               25 2009]
%Y A057427 Sequence in context: A165596 A070238 A103131 this_sequence A057428 A062157 
               A112347
%Y A057427 Adjacent sequences: A057424 A057425 A057426 this_sequence A057428 A057429 
               A057430
%K A057427 easy,nonn,mult
%O A057427 0,1
%A A057427 Henry Bottomley (se16(AT)btinternet.com), Sep 05 2000

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