A218611 -id:A218611 - 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.

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

Original entry on oeis.org

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

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 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.

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 A218787, i.e. a(n) = A057163(A218787(n)). A218786 gives the sizes of these trees. Cf. A072764, A218610, A218611.

A218612 Numbers which are the roots of distinct not-previously-encountered side-trees ("tendrils") sprouting from the side of the infinite beanstalk (see A213730).

Original entry on oeis.org

2, 10, 22, 47, 105, 208, 224, 471, 486, 943, 966, 974, 1934, 1972, 3509, 3546, 3765, 3893, 3930, 3995, 4027, 4049, 7912, 8041, 8058, 8146, 14291, 15315, 15738, 15827, 15995, 16040, 16122, 16211, 16312, 16334, 31694, 32207, 32440, 32462, 32568, 57145, 57208

Offset: 1

Antti Karttunen, Nov 11 2012

nonn

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

A superset of A218548. Cf. A218611, A218613.

(define (A218612 n) (A213730 (A218611 n)))

a(n) = A213730(A218611(n)).

A218613 Sizes of distinct new sidetrees ("tendrils", in the order of their appearance) that sprout along (A218787) the infinite trunk of beanstalk (A179016).

Original entry on oeis.org

0, 1, 2, 3, 2, 5, 6, 4, 4, 5, 5, 9, 10, 17, 17, 5, 19, 32, 6, 10, 8, 4, 3, 10, 33, 4, 5, 7, 34, 20, 31, 5, 62, 4, 7, 4, 5, 14, 33, 7, 54, 32, 12, 14, 3, 34, 47, 4, 8, 31, 32, 143, 10, 11, 17, 169, 13, 240, 59, 8, 7, 15, 18, 12, 33, 102, 5, 66, 116, 6, 11, 15

Offset: 1

Antti Karttunen, Nov 11 2012

nonn

a(n) = A213726(A218612(n))-1. All values A218549(n)-1 occur here at some point and in order.

(define (A218613 n) (A218786 (A218611 n)))

a(n) = A218786(A218611(n)).

A218609 Distinct values of A218787 in the order of appearance.

Original entry on oeis.org

0, 1, 2, 8, 3, 60, 172, 12, 20, 49, 54, 3016, 10096, 125744802, 101035235, 25, 1358590114, 40796719636668219, 70, 19049, 1770, 18, 7, 16261, 82682568533587123, 17, 36, 307, 315899951699378231, 3871315398, 15215587727307698, 59, 9097520004151634187729920190004140

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 left, and larger to the right hand side of each branch.

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

These are the mirror-images of binary trees given in A218610, i.e. a(n) = A057163(A218610(n)). A218613 gives the sizes of these trees. Cf. A218611.

(define (A218609 n) (A218787 (A218611 n)))

a(n) = A218787(A218611(n)).

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

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Author

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Comments

Examples

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A218612 Numbers which are the roots of distinct not-previously-encountered side-trees ("tendrils") sprouting from the side of the infinite beanstalk (see A213730).

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A218613 Sizes of distinct new sidetrees ("tendrils", in the order of their appearance) that sprout along (A218787) the infinite trunk of beanstalk (A179016).

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Formula

A218609 Distinct values of A218787 in the order of appearance.

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Crossrefs

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Scheme

Formula

A218610 Distinct values of A218788 in the order of appearance.

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Scheme

Formula