A218788 a(n) = A014486-index for the n-th tendril of infinite beanstalk (A213730(n)), with the "lesser numbers to the right side" construction.

0, 0, 0, 0, 1, 0, 0, 1, 3, 0, 0, 0, 1, 3, 0, 4, 0, 0, 1, 0, 0, 1, 3, 0, 4, 0, 0, 1, 4, 0, 0, 2, 0, 3, 1, 0, 0, 0, 1, 3, 0, 4, 0, 0, 1, 4, 0, 0, 2, 0, 3, 1, 0, 4, 0, 0, 2, 0, 37, 0, 0, 110, 0, 3, 0, 1, 0, 0, 1, 3, 0, 4, 0, 0, 1, 4, 0, 0, 2, 0, 3, 1, 0, 4, 0, 0

Offset

1,9

Comments

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

Links

A. Karttunen, Table of n, a(n) for n = 1..8727

A. Karttunen, Illustration of how binary trees (the second rightmost column) are encoded by A014486

Example

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).
When we construct a binary tree from this in such a fashion that the larger numbers go to the left, we obtain:
..........
29...28...
..\./.....
...25..24.
....\./...
.....22...
..........
and the binary tree
.......
.\./...
..*....
...\./.
....*..
.......
is located as A014486(3) in the normal encoding order of binary trees, thus a(9)=3.

Prog

(Scheme with Antti Karttunen's memoization macro definec):
(define (A218788 n) (Aux_for218788 (A213730 n)))
(definec (Aux_for218788 n) (cond ((zero? (A079559 n)) 0) ((not (zero? (A213719 n))) -1) (else (A072764bi (Aux_for218788 (A213724 n)) (Aux_for218788 (A213723 n))))))

Crossrefs

These are the mirror-images of binary trees given in A218787, i.e. a(n) = A057163(A218787(n)). A218786 gives the sizes of these trees. Cf. A072764, A218610, A218611.

Sequence in context: A354061 A318921 A114516 * A328969 A027185 A035641

Adjacent sequences: A218785 A218786 A218787 * A218789 A218790 A218791

Keyword

nonn

Author

Antti Karttunen, Nov 11 2012

Status

approved