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 A266640 #13 Jan 29 2016 17:13:51 %S A266640 1,2,1,3,2,1,1,4,3,2,1,2,1,1,1,5,4,3,2,1,3,2,1,2,1,1,2,1,1,1,1,6,5,4, %T A266640 3,2,1,4,3,2,1,3,2,1,2,1,1,3,2,1,2,1,1,2,1,1,1,2,1,1,1,1,1,7,6,5,4,3, %U A266640 2,1,5,4,3,2,1,4,3,2,1,3,2,1,2,1,1,4,3,2,1,3,2,1,2,1,1,3,2,1,2,1,1,2,1,1,1 %N A266640 Reversed reduced frequency counts for A004001: a(n) = A265754(A054429(n)). %C A266640 Deleting all 1's and decrementing the remaining terms by one gives the sequence back. %H A266640 Antti Karttunen, <a href="/A266640/b266640.txt">Table of n, a(n) for n = 1..8191</a> %H A266640 T. Kubo and R. Vakil, <a href="http://dx.doi.org/10.1016/0012-365X(94)00303-Z">On Conway's recursive sequence</a>, Discr. Math. 152 (1996), 225-252. %F A266640 a(n) = A265754(A054429(n)). %F A266640 Other identities. For all n >= 0: %F A266640 a(2^n) = n+1. %e A266640 Illustration how the sequence can be constructed by concatenating the reversed reduced frequency counts R_n of each successive level n of A004001-tree: %e A266640 1 %e A266640 / \ %e A266640 2 1 %e A266640 /|\ \ %e A266640 ____________3 2 1 1 %e A266640 / / / | |\ \ \ %e A266640 ________4 __3 2 1 2 1 1 1 %e A266640 / / / / / / /| /| | |\ \ \ \ %e A266640 5 4 3 2 1 3 2 1 2 1 1 2 1 1 1 1 %e A266640 etc. %o A266640 (Scheme) (define (A266640 n) (A265754 (A054429 n))) %Y A266640 Cf. A004001, A054429. %Y A266640 Cf. A000079 (positions of records, where n appears for the first time). %Y A266640 Cf. A265754 (obtained from the mirror image of the same tree). %K A266640 nonn,tabf %O A266640 1,2 %A A266640 _Antti Karttunen_, Jan 22 2016