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Search: id:A162537
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| A162537 |
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a(n) = the smallest positive multiple of n where every length of the runs of 0's and 1's in the binary representation of a(n) is coprime to n. |
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+0
3
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| 1, 2, 3, 8, 5, 42, 7, 8, 9, 10, 11
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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By "run" of 0's or 1's, it is meant: Think of binary n as a string of 0's and 1's. A single run of the digit b (0 or 1) is made up completely of consecutive digits all equal to b, and is bounded on its ends by either the digit 1-b or by the edge of the string.
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EXAMPLE
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For n = 4, we check. 4 in binary is 100, which has a run of two 0's; and 2 is not coprime to 4. But 2*4 = 8 = 1000 in binary has a run of one 1 and a run of three 0's. Since both 1 and 3 are coprime to 4, then a(4) = 8.
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CROSSREFS
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A162535, A162536
Sequence in context: A091136 A140651 A007955 this_sequence A109844 A128779 A112283
Adjacent sequences: A162534 A162535 A162536 this_sequence A162538 A162539 A162540
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KEYWORD
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base,more,nonn
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Jul 05 2009
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