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A140690
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A positive integer n is included if n written in binary can be subdivided into a number of runs all of equal-length, the first run from the left consisting of all 1's, the next run consisting of all 0's, the next run consisting of all 1's, the next run consisting of all 0's, etc.
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1
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1, 2, 3, 5, 7, 10, 12, 15, 21, 31, 42, 51, 56, 63, 85, 127, 170, 204, 240, 255, 341, 455, 511, 682, 819, 992, 1023, 1365, 2047, 2730, 3276, 3640, 3855, 4032, 4095, 5461, 8191, 10922, 13107, 16256, 16383, 21845, 29127, 31775, 32767, 43690, 52428, 61680
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Also: numbers of the form (2^s-1)*[4^{s*(k+1)}-1]/(4^s-1) or 2^s(2^s-1)*[4^{s*(k+1)}-1]/(4^s-1), s>=1, k>=0. Subsequences are, with the possible exception of terms at n=0, A002450(n), A043291(n), A015565(2n), A093134(2n+1), A000225(n), A020522(n). [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 04 2008]
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EXAMPLE
| 819 in binary is 1100110011. The runs of 0s and 1s are (11)(00)(11)(00)(11). Each run (alternating 1s and 0s) is the same length. So 819 is in the sequence.
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CROSSREFS
| Sequence in context: A119592 A191892 A087539 * A004684 A036607 A062442
Adjacent sequences: A140687 A140688 A140689 * A140691 A140692 A140693
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KEYWORD
| base,nonn
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AUTHOR
| Leroy Quet Jul 11 2008
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EXTENSIONS
| Terms beyond 42 from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Aug 04 2008
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