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%I #9 Aug 11 2015 01:36:15
%S 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 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 1,2,0,3,0,0,1,3,0,0,2,0,2,1,0,3,0,0,2
%N The sizes of the "tendrils" (finite side-trees sprouting at A213730, A218787) of infinite beanstalk (A179016).
%H Antti Karttunen, <a href="/A218786/b218786.txt">Table of n, a(n) for n = 1..8727</a>
%F a(n) = A213726(A213730(n))-1.
%e 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 (Scheme): (define (A218786 n) (-1+ (A213726 (A213730 n))))
%Y Equally, a(n) = A072643(A218787(n)) = A072643(A218788(n)). Cf. A218613, A218603, A218604.
%K nonn
%O 1,9
%A _Antti Karttunen_, Nov 11 2012