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Search: id:A014081
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| A014081 |
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Occurrences of '11' in binary expansion of n. |
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+0
16
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| 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 1, 2, 3, 0, 0, 0, 1, 0, 0, 1, 2, 1, 1, 1, 2, 2, 2, 3, 4, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 1, 2, 3, 1, 1, 1, 2, 1, 1, 2, 3, 2, 2, 2, 3, 3, 3, 4, 5, 0, 0, 0, 1, 0, 0, 1, 2, 0, 0, 0, 1, 1, 1, 2, 3, 0, 0, 0, 1, 0, 0, 1, 2, 1, 1, 1, 2, 2, 2, 3, 4, 1, 1, 1, 2, 1, 1, 2, 3, 1
(list; graph; listen)
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OFFSET
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0,8
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COMMENT
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First occurrence of k: 0, 3, 7, 15, 31, 63, 127, 255, 511, 1023, 2047, 4095, 8191, ..., A000225[k-1]. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 02 2009]
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LINKS
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R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (1).
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics (2).
Index entries for sequences related to binary expansion of n
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FORMULA
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a(4n) = a(4n+1) = a(n), a(4n+2) = a(2n+1), a(4n+3) = a(2n+1) + 1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Aug 21 2003
G.f.: 1/(1-x) * sum(k>=0, t^3/(1+t)/(1+t^2), t=x^2^k). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 10 2003
a(n) = A000120(n) - A069010(n). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 10 2003
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MAPLE
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# To count occurrences of 11..1 (k times) in binary expansion of v:
cn := proc(v, k) local n, s, nn, i, j, som, kk; som := 0;
kk := cat(seq(1, j = 1 .. k)); n := convert(v, binary);
s := convert(n, string); nn := length(s); for i to nn - k + 1 do
if substring(s, i .. i + k - 1) = kk then som := som + 1 fi
od; RETURN(som) end;
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MATHEMATICA
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f[n_] := Count[ Partition[ IntegerDigits[n, 2], 2, 1], {1, 1}]; Table[ f@n, {n, 0, 104}] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 02 2009]
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CROSSREFS
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Cf. A014082, A033264, A037800, A056973.
Sequence in context: A129753 A147693 A070936 this_sequence A091890 A029431 A091492
Adjacent sequences: A014078 A014079 A014080 this_sequence A014082 A014083 A014084
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe (simon.plouffe(AT)gmail.com)
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