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).

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, 54, 56, 58, 60, 62, 63, 16, 61, 17, 59, 18, 57, 19, 55, 20, 53, 21, 51, 22, 49, 23, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 127, 32, 125, 33

Offset: 1

Author

Antti Karttunen, Oct 28 2001

Keywords

• nonn

Comments

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.

Links

• Index entries for sequences that are permutations of the natural numbers

Crossrefs

A057114, A065263, A065275, A065281, A065287. Inverse: A065270, conjugated with A059893: A065271 and the inverse of that: A065272.

Programs

Maple

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;