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A065269 Infinite binary tree inspired permutation of N: 1 -> 1, 11ab..yz -> 11ab..yz0, 10ab..y1 -> 10ab..y, 10ab..y0 -> 11AB..Y1 (where 1AB..Y1 is the complement of 0ab..y0).

%I A065269 #5 May 01 2014 02:42:46
%S A065269 1,3,6,7,2,12,14,15,4,13,5,24,26,28,30,31,8,29,9,27,10,25,11,48,50,52,
%T A065269 54,56,58,60,62,63,16,61,17,59,18,57,19,55,20,53,21,51,22,49,23,96,98,
%U A065269 100,102,104,106,108,110,112,114,116,118,120,122,124,126,127,32,125,33
%N A065269 Infinite binary tree inspired permutation of N: 1 -> 1, 11ab..yz -> 11ab..yz0, 10ab..y1 -> 10ab..y, 10ab..y0 -> 11AB..Y1 (where 1AB..Y1 is the complement of 0ab..y0).
%C A065269 On the right side every node replaces its left child, on the left side the right children replace their parents and the left children are reflected to the right side (becoming right children). See comment at A065263.
%H A065269 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%p A065269 LeftChildInverted := proc(n) local k; if(1 = n) then RETURN(1); fi; k := floor_log_2(n)-1; if(3 = floor(n/(2^k))) then RETURN(2*n); fi; if(1 = (n mod 2)) then RETURN((n-1)/2); fi; RETURN(2^(k+1) + ((2^(k+2))-1) - n); end;
%Y A065269 A057114, A065263, A065275, A065281, A065287. Inverse: A065270, conjugated with A059893: A065271 and the inverse of that: A065272.
%K A065269 nonn
%O A065269 1,2
%A A065269 _Antti Karttunen_, Oct 28 2001