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Search: id:A163382
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| A163382 |
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a(n) = the (decimal equivalent of the) smallest integer that can be made by rotating the binary digits of n any number of positions to the left or right, where a(n) in binary must contain the same number of digits (without any leading 0's) as n written in binary has. |
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+0
3
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| 1, 2, 3, 4, 5, 5, 7, 8, 9, 10, 11, 9, 11, 11, 15, 16, 17, 18, 19, 18, 21, 21, 23, 17, 19, 21, 23, 19, 23, 23, 31, 32, 33, 34, 35, 36, 37, 38, 39, 34, 38, 42, 43, 37, 45, 43, 47, 33, 35, 37, 39, 38, 43, 45, 47, 35, 39, 43, 47, 39, 47, 47, 63, 64, 65, 66, 67, 68, 69, 70, 71, 68, 73
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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By rotating the binary digits of n, it is meant: Write n in binary without any leading 0's. To rotate this string to the right, say, by one position, first remove the rightmost digit and then append it on the left side of the remaining string. (So, the least significant digit becomes the most significant digit.) Here, leading 0's are not removed after the first rotation, so that each binary string being rotated has the same number of binary digits as n has.
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EXAMPLE
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13 in binary is 1101. Rotating this just once to the right, we get 1110, 14 in decimal. If we rotate twice to the right, we would have had 0111 = 7 in decimal. Rotating 3 times, we end up with 1011, which is 11 in decimal. Rotating 4 times, we end up at the beginning with 1101 = 13. 7 is the smallest of these, but it contains a 0 in the leftmost position of its 4-digit binary representation. 11 (decimal), on the other hand, is the smallest with a 1 in the leftmost position of its 4-digit binary representation. So, a(13) = 11.
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CROSSREFS
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Cf. A163380, A163381
Sequence in context: A131233 A136623 A031218 this_sequence A094017 A092762 A017844
Adjacent sequences: A163379 A163380 A163381 this_sequence A163383 A163384 A163385
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KEYWORD
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base,nonn,new
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AUTHOR
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Leroy Quet (q1qq2qqq3qqqq(AT)yahoo.com), Jul 25 2009
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EXTENSIONS
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Corrected and extended by Sean A. Irvine (sairvin(AT)xtra.co.nz), Nov 08 2009
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