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A065263 Infinite binary tree inspired permutation of N: 1 -> 3, 11ab..yz -> 11ab..yz1, 10ab..y0 -> 10ab..y, 10ab..y1 -> 11AB..Y0 (where 1AB..Y0 is the complement of 0ab..y1). 6
3, 1, 7, 2, 6, 13, 15, 4, 14, 5, 12, 25, 27, 29, 31, 8, 30, 9, 28, 10, 26, 11, 24, 49, 51, 53, 55, 57, 59, 61, 63, 16, 62, 17, 60, 18, 58, 19, 56, 20, 54, 21, 52, 22, 50, 23, 48, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 32, 126, 33, 124 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

When an infinite planar binary tree is mapped breadth-first-wise from left to right (1 is at top, 2 is its left and 3 its right child, 4 is 2's left child, etc.) then this permutation induces such rearrangement of its nodes, that on the right side every node replaces its right child, on the left side the left children replace their parents and the right children are reflected to the right side, to be the left children of their new parents.

LINKS

Table of n, a(n) for n=1..67.

Index entries for sequences that are permutations of the natural numbers

MAPLE

RightChildInverted := proc(n) local k; if(1 = n) then RETURN(3); fi; k := floor_log_2(n)-1; if(3 = floor(n/(2^k))) then RETURN((2*n)+1); fi; if(0 = (n mod 2)) then RETURN(n/2); fi; RETURN(2^(k+1) + ((2^(k+2))-1) - n); end;

CROSSREFS

A057114, A065269, A065275, A065281, A065287. Inverse: A065264, conjugated with A059893: A065265 and the inverse of that: A065266.

Sequence in context: A016576 A073874 A065287 * A057114 A235800 A065259

Adjacent sequences:  A065260 A065261 A065262 * A065264 A065265 A065266

KEYWORD

nonn

AUTHOR

Antti Karttunen, Oct 28 2001

STATUS

approved

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Last modified October 19 13:01 EDT 2019. Contains 328222 sequences. (Running on oeis4.)