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Search: id:A055975
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| A055975 |
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First differences of A003188 (decimal equivalent of the Gray Code). |
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+0
4
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| 1, 2, -1, 4, 1, -2, -1, 8, 1, 2, -1, -4, 1, -2, -1, 16, 1, 2, -1, 4, 1, -2, -1, -8, 1, 2, -1, -4, 1, -2, -1, 32, 1, 2, -1, 4, 1, -2, -1, 8, 1, 2, -1, -4, 1, -2, -1, -16, 1, 2, -1, 4, 1, -2, -1, -8, 1, 2, -1, -4, 1, -2, -1, 64, 1, 2, -1, 4, 1, -2, -1, 8, 1, 2, -1, -4, 1, -2, -1, 16, 1, 2, -1, 4, 1, -2, -1, -8, 1, 2, -1, -4, 1, -2, -1, -32, 1, 2, -1, 4
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Multiplicative with a(2^e) = 2^e, a(p^e) = (-1)^((p^e-1)/2) otherwise. Mitch Harris (Harris.Mitchell(AT)mgh.harvard.edu) May 17, 2005.
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LINKS
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N. J. A. Sloane, Transforms
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FORMULA
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a(2n) = 2a(n), a(2n+1) = (-1)^n. G.f. sum(k>=0, 2^k*t/(1+t^2), t=x^2^k). a(n) = 2^A007814(n) * (-1)^((n/2^A007814(n)-1)/2). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 29 2003
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EXAMPLE
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Since A003188(n) is 0 1 3 2 6 7 5 4 12 13 15 14 10 ..., a(n) begins 1 2 -1 4 1 -2 -1 8 1 2 -1 4 ...
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PROGRAM
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(PARI) a(n)=((-1)^((n/2^valuation(n, 2)-1)/2)*2^valuation(n, 2) (from Ralf Stephan)
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CROSSREFS
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The unsigned sequence |a(n)| is A006519(n) = 2^A007814(n)
Cf. A003188, A006519 and A007814.
MASKTRANSi transform of A053644 (conjectural).
Cf. A119972, A119974.
Sequence in context: A068057 A003484 A006519 this_sequence A118827 A118830 A087258
Adjacent sequences: A055972 A055973 A055974 this_sequence A055976 A055977 A055978
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KEYWORD
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easy,nice,sign,mult
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AUTHOR
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Alford Arnold (Alford1940), Jul 22 2000
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EXTENSIONS
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More terms from Larry Reeves (larryr(AT)acm.org), Sep 05 2000
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