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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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Lionel Levine, Fractal sequences and restricted Nim, Ars Combin. 80 (2006), 113-127.
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LINKS
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FORMULA
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a(2^m + k) = f(2^m + f(k)) for m >= 0, 0 <= k < 2^m where f(n) = A059893(n) for n > 0 with f(0) = 0.
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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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PROG
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(PARI) a(n) = if(bitand(n, n-1)==0, n, my(b=logint(n, 2), s=b-logint(n-(1<<b), 2)); (((n - (1<<b)) << 1) + 1) << (s-1)) \\ Andrew Howroyd, Jan 04 2024
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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