A055975 First differences of A003188 (decimal equivalent of the Gray Code).
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
Offset: 1
Examples
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, ... .
Links
- Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
- N. J. A. Sloane, Transforms
- Index entries for sequences related to binary expansion of n
Crossrefs
Programs
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Haskell
a055975 n = a003188 n - a003188 (n-1) a055975_list = zipWith (-) (tail a003188_list) a003188_list -- Reinhard Zumkeller, Apr 28 2012
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Maple
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
f[n_]:=BitXor[n,Floor[n/2]];Differences[Array[f,120,0]] (* Harvey P. Dale, Jul 18 2011, applying Robert G. Wilson v's program from A003188 *)
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PARI
a(n)=((-1)^((n/2^valuation(n,2)-1)/2)*2^valuation(n,2)) \\ Ralf Stephan
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Python
def A055975(n): return (n^(n>>1))-((n-1)^(n-1>>1)) # Chai Wah Wu, Jun 29 2022
Formula
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
a((2*n-1)*2^p) = (-1)^(n+1)*2^p, p >= 0. - Johannes W. Meijer, Jan 27 2013
Extensions
More terms from Larry Reeves (larryr(AT)acm.org), Sep 05 2000
Comments