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A139708
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Take n in binary. Rotate the binary digits to the left until a 1 once again appears as the leftmost digit. Convert back into decimal for a(n).
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8
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1, 2, 3, 4, 6, 5, 7, 8, 12, 10, 14, 9, 11, 13, 15, 16, 24, 20, 28, 18, 22, 26, 30, 17, 19, 21, 23, 25, 27, 29, 31, 32, 48, 40, 56, 36, 44, 52, 60, 34, 38, 42, 46, 50, 54, 58, 62, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 64, 96, 80, 112, 72, 88, 104, 120
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OFFSET
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1,2
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COMMENTS
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This sequence written in binary is A139709.
This is a permutation of the positive integers. A139706 is the inverse permutation.
Moreover, the first 2^n terms are a permutation of the first 2^n positive integers. Fixed points of the permutation are A272919. - Ivan Neretin, May 10 2016
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REFERENCES
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L. Levine, Fractal sequences and restricted Nim, Ars Combin. 80 (2006), 113-127.
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LINKS
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Ivan Neretin, Table of n, a(n) for n = 1..8192
L. Levine, Fractal sequences and restricted Nim, arXiv:math/0409408 [math.CO], 2004.
Index entries for sequences that are permutations of the natural numbers
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MAPLE
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A139708 := proc(n) local a; a := ListTools[Rotate](convert(n, base, 2), -1) ; while op(-1, a) = 0 do a := ListTools[Rotate](a, -1) ; od: add(op(i, a)*2^(i-1), i=1..nops(a)) : end: seq(A139708(n), n=1..100) ; # R. J. Mathar, May 04 2008
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MATHEMATICA
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rbd[n_]:=Module[{idn2=RotateLeft[IntegerDigits[n, 2]]}, While[ idn2[[1]] ==0, idn2= RotateLeft[ idn2]]; FromDigits[idn2, 2]]; Array[rbd, 80] (* Harvey P. Dale, Jun 07 2015 *)
Table[FromDigits[RotateLeft[d = IntegerDigits[n, 2], Position[Join[d, d], 1][[2, 1]] - 1], 2], {n, 71}] (* Ivan Neretin, May 10 2016 *)
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CROSSREFS
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Cf. A139706 (inverse), A139709 (in binary), A272919 (fixed points).
Sequence in context: A139706 A333777 A306869 * A333776 A305410 A059893
Adjacent sequences: A139705 A139706 A139707 * A139709 A139710 A139711
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KEYWORD
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nonn,base,easy
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AUTHOR
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Leroy Quet, Apr 30 2008
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EXTENSIONS
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More terms from R. J. Mathar, May 04 2008
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STATUS
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approved
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