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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).

%I A065263 #5 May 01 2014 02:42:45
%S A065263 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 A065263 55,57,59,61,63,16,62,17,60,18,58,19,56,20,54,21,52,22,50,23,48,97,99,
%U A065263 101,103,105,107,109,111,113,115,117,119,121,123,125,127,32,126,33,124
%N 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).
%C A065263 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 A065263 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%p A065263 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 A065263 A057114, A065269, A065275, A065281, A065287. Inverse: A065264, conjugated with A059893: A065265 and the inverse of that: A065266.
%K A065263 nonn
%O A065263 1,1
%A A065263 _Antti Karttunen_, Oct 28 2001