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A054429
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Simple self-inverse permutation of natural numbers: List each block of 2^n numbers (from 2^n to 2^(n+1) - 1) in reverse order.
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47
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1, 3, 2, 7, 6, 5, 4, 15, 14, 13, 12, 11, 10, 9, 8, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20, 19, 18, 17, 16, 63, 62, 61, 60, 59, 58, 57, 56, 55, 54, 53, 52, 51, 50, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 127, 126, 125, 124, 123, 122, 121
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) gives the position of the inverse of the n-th term in the full Stern Brocot tree: A007305(a(n)+2)=A047679(n) and A047679(a(n))=A007305(n+2). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Dec 22 2008]
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LINKS
| R. Zumkeller, Table of n, a(n) for n = 1..10000
R. Stephan, Some divide-and-conquer sequences ...
R. Stephan, Table of generating functions
Index entries for sequences that are permutations of the natural numbers
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FORMULA
| a(n) = ReflectBinTreePermutation(n)
a(n) = if n=1 then 1 else 2*a(floor(n/2)) + 1 - n mod 2. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Feb 18 2003
1/(1-x) * ((x-2x^2)/(1-x) + sum(k>=0, 3*2^k*x^2^k)). - Ralf Stephan (ralf(AT)ark.in-berlin.de), Sep 15 2003
A000120(a(n)) = A000120(A059894(n)) = A023416(n) + 1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 05 2003
A115310(n, 1) = a(n). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jan 20 2006
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MAPLE
| ReflectBinTreePermutation := n -> (((3*(2^floor_log_2(n)))-n)-1); # floor_log_2(x) gives [log2(x)], but floor(log[2](x)) is not healthy in Maple, so use this:
floor_log_2 := proc(n) local nn, i; nn := n; for i from -1 to n do if(0 = nn) then RETURN(i); fi: nn := floor(nn/2); od; end;
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CROSSREFS
| See also A054424, A054430.
{A000027, A054429, A059893, A059894} form a 4-group.
Cf. A115303, A115304, A115305, A115306, A115307, A115308, A115309, A106649.
This is Guy Steele's sequence GS(6, 5) (see A135416).
Sequence in context: A130328 A083569 A071574 * A126316 A101224 A139285
Adjacent sequences: A054426 A054427 A054428 * A054430 A054431 A054432
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KEYWORD
| nonn,easy
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AUTHOR
| Antti Karttunen
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