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A055975
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First differences of A003188 (decimal equivalent of the Gray Code).
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10
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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
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listen;
history;
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internal format)
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OFFSET
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1,2
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COMMENTS
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Multiplicative with a(2^e) = 2^e, a(p^e) = (-1)^((p^e-1)/2) otherwise. - Mitch Harris, May 17 2005
In the binary representation of n, clear everything left of the least significant 1 bit, and negate if the bit left of it was set originally. - Ralf Stephan, Aug 23 2013
This sequence is the trace of n in the minimal alternating binary representation of n (defined at A256696). - Clark Kimberling, Apr 07 2015
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LINKS
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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, Oct 29 2003
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EXAMPLE
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Since A003188 is 0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 15, 14, 10, ...,
sequence begins 1, 2, -1, 4, 1, -2, -1, 8, 1, 2, -1, 4, ... .
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MAPLE
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nmax:=100: for p from 0 to ceil(simplify(log[2](nmax))) do for n from 1 to ceil(nmax/(p+2)) do a((2*n-1)*2^p) := (-1)^(n+1)*2^p od: od: seq(a(n), n=1..nmax); # Johannes W. Meijer, Jan 27 2013
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MATHEMATICA
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PROG
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(PARI)
a(n)=((-1)^((n/2^valuation(n, 2)-1)/2)*2^valuation(n, 2)) \\ Ralf Stephan
(Haskell)
a055975 n = a003188 n - a003188 (n-1)
a055975_list = zipWith (-) (tail a003188_list) a003188_list
(Python)
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CROSSREFS
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MASKTRANSi transform of A053644 (conjectural).
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KEYWORD
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easy,nice,sign,mult
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AUTHOR
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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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STATUS
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approved
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