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 A218786 #12 Aug 29 2025 18:51:37 %S A218786 0,0,0,0,1,0,0,1,2,0,0,0,1,2,0,3,0,0,1,0,0,1,2,0,3,0,0,1,3,0,0,2,0,2, %T A218786 1,0,0,0,1,2,0,3,0,0,1,3,0,0,2,0,2,1,0,3,0,0,2,0,5,0,0,6,0,2,0,1,0,0, %U A218786 1,2,0,3,0,0,1,3,0,0,2,0,2,1,0,3,0,0,2 %N A218786 The sizes of the "tendrils" (finite side-trees sprouting at A213730, A218787) of infinite beanstalk (A179016). %H A218786 Antti Karttunen, <a href="/A218786/b218786.txt">Table of n, a(n) for n = 1..8727</a> %F A218786 a(n) = A213726(A213730(n))-1. %e A218786 The first four tendrils of the beanstalk sprout at 2, 5, 6 and 9, (the first four nonzero terms of A213730) which are all leaves (i.e., in A055938), thus the first four terms of this sequence are all 0's. The next term A213730(5)=10, which is not leaf, but branches to two leaf-branches (12 and 13, as with both we have: 12-A000120(12)=10 and 13-A000120(13)=10, and both 12 and 13 are found from A055938, so the tendril at 10 is a binary tree of one internal vertex (and two leaves), i.e., \/, thus a(5)=1. %o A218786 (Scheme) (define (A218786 n) (-1+ (A213726 (A213730 n)))) %Y A218786 Equally, a(n) = A072643(A218787(n)) = A072643(A218788(n)). Cf. A218613, A218603, A218604. %K A218786 nonn,changed %O A218786 1,9 %A A218786 _Antti Karttunen_, Nov 11 2012