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 A074683 #11 Jun 01 2025 23:59:09 %S A074683 0,1,3,2,7,6,8,5,4,17,16,18,15,14,20,19,22,12,11,21,13,10,9,45,44,46, %T A074683 43,42,48,47,50,40,39,49,41,38,37,54,53,55,52,51,61,60,63,31,30,62,32, %U A074683 29,28,57,56,64,34,33,59,36,26,25,58,35,27,24,23,129,128,130,127,126 %N A074683 Permutation of natural numbers induced by the Catalan Automorphism *A074683 acting on parenthesizations as encoded and ordered by A014486/A063171. %C A074683 This bijection maps between the "standard" ordering of binary trees as encoded by A014486 and "variant A quaternary encoding" as explained in the sequence A085184. %C A074683 This is a rare example of Catalan Automorphism (with simple definition) where the cycle count sequence (A089411) is not monotone. (See A127296 for more complex example.) %H A074683 A. Karttunen, <a href="http://oeis.org/wiki/Catalan_Automorphisms">Catalan Automorphisms</a> %H A074683 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %o A074683 (Scheme function implementing this automorphism on list-structures/S-expressions:) (define (*A074683! s) (cond ((pair? s) (*A074683! (car s)) (*A074683! (cdr s)) (*A074679! s))) s) %Y A074683 Row 12 of A122202. Inverse of A074684. a(n) = A057163(A074682(A057163(n))). %Y A074683 The number of cycles, maximum cycle sizes and LCM's of all cycle sizes in subpermutations limited by A014137 and A014138 are given by A089411, A086586 and A089412. %K A074683 nonn %O A074683 0,3 %A A074683 _Antti Karttunen_, Sep 11 2002