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A103185
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a(n) = Sum_{ k >= 0 such that n + k == 0 mod 2^k } 2^(k-1).
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6
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0, 1, 2, 1, 0, 5, 2, 1, 0, 1, 2, 1, 8, 5, 2, 1, 0, 1, 2, 1, 0, 5, 2, 1, 0, 1, 2, 17, 8, 5, 2, 1, 0, 1, 2, 1, 0, 5, 2, 1, 0, 1, 2, 1, 8, 5, 2, 1, 0, 1, 2, 1, 0, 5, 2, 1, 0, 1, 34, 17, 8, 5, 2, 1, 0, 1, 2, 1, 0, 5, 2, 1, 0, 1, 2, 1, 8, 5, 2, 1, 0, 1, 2, 1, 0, 5, 2, 1, 0, 1, 2, 17, 8, 5, 2, 1, 0, 1, 2, 1, 0, 5, 2, 1
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,3
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LINKS
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David Applegate, Benoit Cloitre, Philippe Deléham and N. J. A. Sloane, Sloping binary numbers: a new sequence related to the binary numbers [pdf, ps].
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FORMULA
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MATHEMATICA
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f[n_] := Block[{k = 1, s = 0, l = Max[2, Floor[ Log[2, n + 1] + 2]]}, While[k < l, If[ Mod[n + k, 2^k] == 0, s = s + 2^(k - 1)]; k++ ]; s]; Table[ f[n], {n, 0, 103}] (* Robert G. Wilson v, Mar 18 2005 *)
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PROG
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(PARI) A103185(n)=(sum(k=0, ceil(log(n+1)/log(2)), if((n+k)%2^k, 0, 2^k))-1)/2 \\ Benoit Cloitre, Mar 20 2005
(Python)
def a102370(n): return 0 if n<1 else sum([(n + k)&(2**k) for k in range(len(bin(n)[2:]) + 1)])
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CROSSREFS
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KEYWORD
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nonn,easy,base
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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