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%I #5 May 01 2014 02:42:45
%S 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,
%T 55,57,59,61,63,16,62,17,60,18,58,19,56,20,54,21,52,22,50,23,48,97,99,
%U 101,103,105,107,109,111,113,115,117,119,121,123,125,127,32,126,33,124
%N 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).
%C 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.
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%p 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;
%Y A057114, A065269, A065275, A065281, A065287. Inverse: A065264, conjugated with A059893: A065265 and the inverse of that: A065266.
%K nonn
%O 1,1
%A _Antti Karttunen_, Oct 28 2001
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