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A165413
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a(n) = number of distinct lengths of runs in the binary representation of n.
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2
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1, 1, 1, 2, 1, 2, 1, 2, 2, 1, 2, 1, 2, 2, 1, 2, 2, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 2, 2, 2, 3, 2, 2, 2, 3, 2, 2, 1, 2, 2, 2, 2, 2, 2, 3, 2, 1, 2, 2, 2, 3, 1, 3, 2, 3, 2, 2, 2, 1, 2, 2, 2, 3, 3, 2, 3, 2, 3, 2, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 3, 2, 2, 2, 2, 3, 3, 2, 2, 2, 2, 2, 3, 2
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,4
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COMMENTS
| Least k whose value is n: 1, 4, 35, 536, 16775, 1060976, ..., . [From Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 30 2009]
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EXAMPLE
| 92 in binary is 1011100. There is a run of one 1, followed by a run of one 0, then a run of three 1's, then finally a run of two 0's. The run lengths are therefore (1,1,3,2). The distinct values of these run lengths are (1,3,2). Since there are 3 distinct values, then a(92) = 3.
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MATHEMATICA
| f[n_] := Length@ Union@ Map[ Length, Split@ IntegerDigits[n, 2]]; Array[f, 105] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 30 2009]
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CROSSREFS
| A005811, A165414
a(n)==1 for A140690. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 30 2009]
Sequence in context: A023518 A022921 A080763 * A172155 A080573 A186440
Adjacent sequences: A165410 A165411 A165412 * A165414 A165415 A165416
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KEYWORD
| base,nonn
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AUTHOR
| Leroy Quet, Sep 17 2009
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EXTENSIONS
| More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Sep 30 2009
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