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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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2
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1, 2, 3, 8, 5, 42, 7, 8, 9, 10, 11, 672, 13, 14, 15, 32, 17, 522, 19, 40, 21, 682, 23, 672, 25, 130, 27, 56, 29, 2730, 31, 32, 33, 34, 35, 8352, 37, 190, 195, 40, 41, 42, 43, 2728, 45, 46, 47, 672, 49, 650, 51, 520, 53, 702, 55, 56, 171, 58, 59, 174720, 61, 62, 189, 128, 195, 8382, 67, 136, 207, 910, 71, 8352, 73, 3626, 75
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| 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
| A162535, A162536
Sequence in context: A184392 A007955 A170826 * A109844 A128779 A112283
Adjacent sequences: A162534 A162535 A162536 * A162538 A162539 A162540
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KEYWORD
| base,nonn
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AUTHOR
| Leroy Quet, Jul 05 2009
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EXTENSIONS
| More terms from Sean A. Irvine (sairvin(AT)xtra.co.nz), Jan 27 2011
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