A213732 -id:A213732 - cp's OEIS frontend

A213733 Positions of odd numbers in A179016.

1, 2, 4, 6, 7, 9, 10, 12, 14, 15, 18, 19, 20, 21, 23, 24, 27, 28, 29, 31, 32, 34, 38, 40, 41, 44, 45, 46, 48, 49, 51, 56, 57, 59, 60, 61, 62, 63, 64, 67, 68, 70, 71, 74, 75, 76, 78, 79, 81, 86, 87, 89, 90, 91, 92, 93, 94, 97, 99, 100, 102, 103, 104, 105, 106

Offset: 1

Antti Karttunen, Nov 01 2012

nonn

These are exactly the positions in the infinite trunk of beanstalk (see A179016 and A213729) where the node is the larger of the two possible branches from one node below. See the explanation at example-lines.

			A179016(1) = 1 is the first case where the infinite trunk has continued to the larger of two branches of the predecessor node. (In this case the predecessor node is A179016(0)=0, for which hold both 0+A000120(0)=0+0=0 (the smaller branch, leading exceptionally back to the same node) and 0+A000120(1)=0+1=1 (the larger branch). Thus the first term of this sequence is 1.
A179016(2) = 3 is the second case where the infinite trunk has continued to the larger of two branches of the predecessor node (In this case the predecessor node is A179016(1)=1, for which hold both 1+A000120(2)=1+1=2 (the smaller branch) and 1+A000120(3)=1+2=3 (the larger branch). Thus the second term of this sequence is 2.

Antti Karttunen, Table of n, a(n) for n = 1..10000

Complement of A213732. First differences: A218775. Characteristic function: A213729.

Scheme
```
: (define (A213733 n) (1+ (A218773 n)))
```

a(n) = A218773(n)+1.

Description changed because of the changed starting offset of A179016. - Antti Karttunen, Nov 05 2012

A218607 The positions of zeros in A218603, i.e., those integers i for which A179016(i) = A213708(i).

Original entry on oeis.org

0, 1, 3, 5, 8, 13, 22, 33, 35, 36, 37, 39, 50, 52, 53, 54, 55, 58, 69, 80, 82, 83, 84, 85, 88, 101, 118, 123, 134, 136, 137, 138, 139, 142, 155, 172, 179, 196, 207, 212, 221, 232, 234, 235, 236, 237, 240, 253, 270, 277, 294, 305, 310, 321, 338, 349, 354, 369, 374, 383, 400

Offset: 0

Antti Karttunen, Nov 10 2012

nonn

These are the points i for which the corresponding node in the infinite trunk of beanstalk (A179016(i)) is at the least possible position of its allotted "window" which it at that point must pass through, i.e., there are no leaves or side-trees at its left (lesser) side at these points. (See comments at A218603.)

Antti Karttunen, Table of n, a(n) for n = 0..7948

Apart from first two terms, a subset of A213732. Cf. A218608, A218605.

A218772 Positions in the infinite trunk of beanstalk (see A179016) where the next node upwards is the smaller of the two possible branches.

Original entry on oeis.org

2, 4, 7, 10, 12, 15, 16, 21, 24, 25, 29, 32, 34, 35, 36, 38, 41, 42, 46, 49, 51, 52, 53, 54, 57, 64, 65, 68, 71, 72, 76, 79, 81, 82, 83, 84, 87, 94, 95, 97, 100, 107, 108, 109, 113, 114, 115, 116, 117, 120, 122, 125, 126, 130, 133, 135, 136, 137, 138, 141, 148

Offset: 1

Antti Karttunen, Nov 05 2012

nonn

			A179016(2) = 3 is the first case where the next term A179016(3) = 4 is the smaller of two branches from 3 (the larger is 5, as 5 = 3+A000120(5)), thus the first term of this sequence is 2.
The next case occurs at A179016(4) = 7, as the next term here is again 8, the smaller of two branches from 7 (the larger being 9, as 9 = 7+A000120(9)), thus the second term of this sequence is 4.

Antti Karttunen, Table of n, a(n) for n = 1..10000

Characteristic function: A213728 shifted once left. Complement: A218773. a(n) = A213732(n)-1. First differences: A218774.

A218774 First differences of A218772.

Original entry on oeis.org

2, 3, 3, 2, 3, 1, 5, 3, 1, 4, 3, 2, 1, 1, 2, 3, 1, 4, 3, 2, 1, 1, 1, 3, 7, 1, 3, 3, 1, 4, 3, 2, 1, 1, 1, 3, 7, 1, 2, 3, 7, 1, 1, 4, 1, 1, 1, 1, 3, 2, 3, 1, 4, 3, 2, 1, 1, 1, 3, 7, 1, 2, 3, 7, 1, 1, 4, 1, 1, 1, 1, 3, 1, 3, 7, 1, 1, 4, 1, 1, 1, 1, 2, 5, 1, 1, 1

Offset: 1

Antti Karttunen, Nov 05 2012

Antti Karttunen, Table of n, a(n) for n = 1..10000

Also the first differences of A213732. Cf. A218775, A218544, A218545.

(define (A218774 n) (- (A218772 (1+ n)) (A218772 n)))

a(n) = A218772(n+1)-A218772(n).

cp's OEIS Frontend

A213733 Positions of odd numbers in A179016.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Scheme

Formula

Extensions

A218607 The positions of zeros in A218603, i.e., those integers i for which A179016(i) = A213708(i).

Views

Author

Keywords

Comments

Links

Crossrefs

A218772 Positions in the infinite trunk of beanstalk (see A179016) where the next node upwards is the smaller of the two possible branches.

Views

Author

Keywords

Examples

Links

Crossrefs

A218774 First differences of A218772.

Views

Author

Keywords

Links

Crossrefs

Programs

Scheme

Formula