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Search: id:A068076
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| A068076 |
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Number of positive integers < n with the same number of 1's in their binary expansions as n. |
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+0
5
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| 0, 1, 0, 2, 1, 2, 0, 3, 3, 4, 1, 5, 2, 3, 0, 4, 6, 7, 4, 8, 5, 6, 1, 9, 7, 8, 2, 9, 3, 4, 0, 5, 10, 11, 10, 12, 11, 12, 5, 13, 13, 14, 6, 15, 7, 8, 1, 14, 16, 17, 9, 18, 10, 11, 2, 19, 12, 13, 3, 14, 4, 5, 0, 6, 15, 16, 20, 17, 21, 22, 15, 18, 23, 24, 16, 25, 17, 18, 6, 19, 26, 27, 19
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OFFSET
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1,4
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EXAMPLE
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The binary expansion of 22 (10110) has 3 1's, as do those of the 6 smaller numbers 7, 11, 13, 14, 19, and 21, so a(22)=6.
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MATHEMATICA
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w[n_] := Plus@@IntegerDigits[n, 2]; a[n_] := Plus@@MapThread[Binomial, {Flatten[Position[Reverse[IntegerDigits[n, 2]], 1]]-1, Range[w[n]]}]
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CROSSREFS
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Cf. A067587, also A000120 for numerous references.
Adjacent sequences: A068073 A068074 A068075 this_sequence A068077 A068078 A068079
Sequence in context: A102587 A119387 A055941 this_sequence A138498 A050319 A132456
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KEYWORD
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nonn
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AUTHOR
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Dean Hickerson (dean(AT)math.ucdavis.edu), Feb 16 2002
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EXTENSIONS
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Edited by John W. Layman (layman(AT)math.vt.edu), Feb 20 2002
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