A218609 -id:A218609 - cp's OEIS frontend

A218787 a(n) = A014486-index for the n-th tendril of infinite beanstalk (A213730(n)), with the "lesser numbers to the left side" construction.

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, 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, 0, 1, 2, 0, 8, 0, 0, 1, 8, 0, 0, 3, 0, 2, 1, 0, 8, 0, 0

Offset: 1

Antti Karttunen, Nov 11 2012

nonn

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

			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 lesser numbers go to the left, we obtain:
...........
...28...29.
.....\./...
..24..25...
...\ /.....
....22.....
...........
and the binary tree
........
...\./..
....*...
.\./....
..*.....
........
is located as A014486(2) in the normal encoding order of binary trees, thus a(9)=2.

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

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.

A218611 Positions in A218787 and A218788 of successive distinct values.

Original entry on oeis.org

1, 5, 9, 16, 32, 59, 62, 115, 118, 208, 212, 213, 384, 389, 649, 654, 686, 703, 708, 716, 720, 723, 1310, 1326, 1328, 1338, 2236, 2369, 2422, 2432, 2452, 2458, 2466, 2476, 2486, 2488, 4545, 4601, 4625, 4627, 4637, 7811, 7817, 7819, 7826, 8287, 8511, 8526, 8631

Offset: 1

Antti Karttunen, Nov 11 2012

nonn

The terms give the positions to A213730 where for the first time a new, never-before-encountered sidetree ("tendril") appears from the side of the infinite beanstalk. See A179016, A218609 and also A218612.

Antti Karttunen, Table of n, a(n) for n = 1..72

Cf. A218609, A218610, A218612, A218613.

A218610 Distinct values of A218788 in the order of appearance.

Original entry on oeis.org

0, 1, 3, 4, 2, 37, 110, 18, 11, 32, 33, 4755, 16127, 73542063, 97105360, 62, 1306632183, 39288694215537689, 193, 8150, 719, 12, 5, 13505, 246941338376004599, 13, 45, 407, 944077158106260984, 4975012595, 5738426278308884, 26, 27439590092251146768825651348524279

Offset: 1

Antti Karttunen, Nov 11 2012

nonn

a(n) = A014486-index for the n-th tendril of the infinite beanstalk (A179016), which has not been encountered before, constructed with lesser numbers coming to the right, and larger to the left hand side of each branch.

A. Karttunen, Table of n, a(n) for n = 1..72
A. Karttunen, Illustration of how binary trees (the second rightmost column) are encoded by A014486

These are the mirror-images of binary trees given in A218609, i.e. a(n) = A057163(A218609(n)). A218613 gives the sizes of these trees. Cf. A218611.

(define (A218610 n) (A218788 (A218611 n)))

a(n) = A218788(A218611(n)).

cp's OEIS Frontend

A218787 a(n) = A014486-index for the n-th tendril of infinite beanstalk (A213730(n)), with the "lesser numbers to the left side" construction.

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A218611 Positions in A218787 and A218788 of successive distinct values.

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A218610 Distinct values of A218788 in the order of appearance.

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