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 A218787 #15 Nov 12 2012 18:00:21 %S A218787 0,0,0,0,1,0,0,1,2,0,0,0,1,2,0,8,0,0,1,0,0,1,2,0,8,0,0,1,8,0,0,3,0,2, %T A218787 1,0,0,0,1,2,0,8,0,0,1,8,0,0,3,0,2,1,0,8,0,0,3,0,60,0,0,172,0,2,0,1,0, %U A218787 0,1,2,0,8,0,0,1,8,0,0,3,0,2,1,0,8,0,0 %N A218787 a(n) = A014486-index for the n-th tendril of infinite beanstalk (A213730(n)), with the "lesser numbers to the left side" construction. %C A218787 "Tendrils" of the beanstalk are the finite side-trees sprouting from its infinite trunk (see A179016) at the numbers given by A213730. %H A218787 A. Karttunen, <a href="/A218787/b218787.txt">Table of n, a(n) for n = 1..8727</a> %H A218787 A. Karttunen, <a href="/A014486/a014486_1.pdf">Illustration of how binary trees (the second rightmost column) are encoded by A014486</a> %e A218787 A213730(9)=22, and from that branches 24 and 25 (as both A011371(24)=A011371(25)=22) and while 24 is a leaf (in A055938) the other branch 25 further branches to two leaves (as both A011371(28)=A011371(29)=25). %e A218787 When we construct a binary tree from this in such a fashion that the lesser numbers go to the left, we obtain: %e A218787 ........... %e A218787 ...28...29. %e A218787 .....\./... %e A218787 ..24..25... %e A218787 ...\ /..... %e A218787 ....22..... %e A218787 ........... %e A218787 and the binary tree %e A218787 ........ %e A218787 ...\./.. %e A218787 ....*... %e A218787 .\./.... %e A218787 ..*..... %e A218787 ........ %e A218787 is located as A014486(2) in the normal encoding order of binary trees, thus a(9)=2. %o A218787 (Scheme with _Antti Karttunen_'s memoization macro definec): %o A218787 (define (A218787 n) (Aux_for218787 (A213730 n))) %o A218787 (definec (Aux_for218787 n) (cond ((zero? (A079559 n)) 0) ((not (zero? (A213719 n))) -1) (else (A072764bi (Aux_for218787 (A213723 n)) (Aux_for218787 (A213724 n)))))) %Y A218787 These are the mirror-images of binary trees given in A218788, i.e. a(n) = A057163(A218788(n)). A218786 gives the sizes of these trees. Cf. A072764, A218609, A218611. %K A218787 nonn %O A218787 1,9 %A A218787 _Antti Karttunen_, Nov 11 2012