This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A072635 #6 May 01 2014 02:43:28 %S A072635 0,1,3,2,6,8,7,19,16,5,15,4,14,52,43,51,42,20,22,53,60,21,61,56,179, %T A072635 155,178,154,177,164,557,163,556,11,39,13,41,151,123,153,125,12,40,33, %U A072635 117,152,124,471,381,477,553,479,555,505,1797,507,1799,478,554,1536 %N A072635 Inverse permutation to A072634. %H A072635 A. Karttunen, <a href="http://www.iki.fi/~kartturi/matikka/Nekomorphisms/gatomorf.htm">Gatomorphisms</a> %H A072635 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %o A072635 (Scheme functions below show the essential idea. For a complete source, follow the "Gatomorphisms" link.) %o A072635 (define A072635 (arithrank->lexrank-bijection A059905 A059906)) %o A072635 (define (arithrank->lexrank-bijection pr1 pr2) (lambda (n) (CatalanRankGlobal (parenthesization->binexp (unrank-bintree n pr1 pr2))))) %o A072635 (define (unrank-bintree rank pr1 pr2) (cond ((zero? rank) (list)) (else (cons (unrank-bintree (pr1 (-1+ rank)) pr1 pr2) (unrank-bintree (pr2 (-1+ rank)) pr1 pr2))))) %o A072635 (define (A059905 n) (if (zero? n) n (+ (modulo n 2) (* 2 (A059905 (floor->exact (/ n 4))))))) %o A072635 (define (A059906 n) (A059905 (floor->exact (/ n 2)))) %Y A072635 A072644 gives the size of the corresponding parenthesizations, i.e. A072644(n) = A029837(A014486(A072635(n))+1)/2 [A029837(n+1) gives the binary width of n]. %Y A072635 A072635(n) = A057163(A072637(n)). Cf. also A014486, A059905, A059906, A071652, A072647, A072637. %K A072635 nonn %O A072635 0,3 %A A072635 _Antti Karttunen_, Jun 02 2002