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Search: id:A057427
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| A057427 |
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Sign(n): a(n) = 1 if n>0, = -1 if n<0, = 0 if n = 0. |
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+0
52
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| 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
(list; graph; listen)
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OFFSET
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0,1
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COMMENT
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For nonnegative n, partial sums of A063524 (characteristic function of 1). - Jeremy Gardiner (jeremy.gardiner(AT)btinternet.com), Sep 08 2002
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]
a(A000027(n)) = 1; a(A000004(n)) = 0. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Oct 11 2008]
Central terms of the triangle in A152487. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 06 2008]
n-th prime mod 2 (with offset 1,1). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Apr 04 2009]
(1-(-1)^nth prime)/2. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 25 2009]
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REFERENCES
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T. M. Macrobert, Functions of a Complex Variable, 4th ed., Macmillan and Co, London, 1958, p. 90
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LINKS
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Index entries for sequences related to linear recurrences with constant coefficients
Index entries for characteristic functions
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FORMULA
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G.f.: x/(1-x).
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)
G.f.: Sum_{k>=0} 2^k x^(2^k)/(1+x^(2^k)). - Michael Somos Sep 11 2005
a(n)=(1-(-1)^A000040(n))/2. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 25 2009]
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PROGRAM
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(PARI) a(n)=sign(n)
(PARI) /* n>=0 */ a(n)=!!n [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 19 2009]
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CROSSREFS
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Cf. A000007. [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), Mar 19 2009]
Cf. A000040. [From Juri-Stepan Gerasimov (2stepan(AT)rambler.ru), Oct 25 2009]
Sequence in context: A165596 A070238 A103131 this_sequence A057428 A062157 A112347
Adjacent sequences: A057424 A057425 A057426 this_sequence A057428 A057429 A057430
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KEYWORD
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easy,nonn,mult
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AUTHOR
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Henry Bottomley (se16(AT)btinternet.com), Sep 05 2000
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