%I #5 May 01 2014 02:43:28
%S 0,1,2,3,6,4,5,14,15,7,16,8,19,42,43,51,52,11,9,39,37,10,28,38,112,
%T 123,121,151,149,122,376,150,466,20,53,17,44,154,155,126,127,18,47,54,
%U 156,135,136,480,481,477,475,387,385,476,1531,386,1234,415,413,1542,1540
%N Inverse permutation to A072636.
%H A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> (Includes the complete Scheme source for computing this sequence)
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%o (Scheme code otherwise as for A072635, but with "transposed coordinates":)
%o (define A072637 (arithrank->lexrank-bijection A059906 A059905))
%Y A072644 gives the size of the corresponding parenthesizations, i.e. A072644(n) = A029837(A014486(A072637(n))+1)/2 [A029837(n+1) gives the binary width of n].
%Y A072637(n) = A057163(A072635(n)). Cf. also A014486, A059905, A059906, A071654, A072646.
%K nonn
%O 0,3
%A _Antti Karttunen_, Jun 02 2002