login
a(n) = A014486-index for the n-th tendril of infinite beanstalk (A213730(n)), with the "lesser numbers to the left side" construction.
15

%I #15 Nov 12 2012 18:00:21

%S 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 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 0,1,2,0,8,0,0,1,8,0,0,3,0,2,1,0,8,0,0

%N a(n) = A014486-index for the n-th tendril of infinite beanstalk (A213730(n)), with the "lesser numbers to the left side" construction.

%C "Tendrils" of the beanstalk are the finite side-trees sprouting from its infinite trunk (see A179016) at the numbers given by A213730.

%H A. Karttunen, <a href="/A218787/b218787.txt">Table of n, a(n) for n = 1..8727</a>

%H A. Karttunen, <a href="/A014486/a014486_1.pdf">Illustration of how binary trees (the second rightmost column) are encoded by A014486</a>

%e 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 When we construct a binary tree from this in such a fashion that the lesser numbers go to the left, we obtain:

%e ...........

%e ...28...29.

%e .....\./...

%e ..24..25...

%e ...\ /.....

%e ....22.....

%e ...........

%e and the binary tree

%e ........

%e ...\./..

%e ....*...

%e .\./....

%e ..*.....

%e ........

%e is located as A014486(2) in the normal encoding order of binary trees, thus a(9)=2.

%o (Scheme with _Antti Karttunen_'s memoization macro definec):

%o (define (A218787 n) (Aux_for218787 (A213730 n)))

%o (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 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 nonn

%O 1,9

%A _Antti Karttunen_, Nov 11 2012