A218774 -id:A218774 - cp's OEIS frontend

A213732 Positions of even numbers greater than zero in A179016.

3, 5, 8, 11, 13, 16, 17, 22, 25, 26, 30, 33, 35, 36, 37, 39, 42, 43, 47, 50, 52, 53, 54, 55, 58, 65, 66, 69, 72, 73, 77, 80, 82, 83, 84, 85, 88, 95, 96, 98, 101, 108, 109, 110, 114, 115, 116, 117, 118, 121, 123, 126, 127, 131, 134, 136, 137, 138, 139, 142, 149

Offset: 1

Antti Karttunen, Nov 01 2012

nonn

These are exactly those positions in the infinite trunk of beanstalk (see A179016 and A213729) where the node is the smaller of the two possible branches from one node below.

			A179016(3) = 4 is the first case where the infinite trunk has continued to the smaller of two branches of the predecessor node. (In this case the predecessor node is A179016(2)=3, for which hold both 3+A000120(4)=3+1=4 (the smaller branch) and 3+A000120(5)=3+2=5 (the larger branch). Thus the first term of this sequence is 3.
A179016(5) = 8 is the second case where the infinite trunk has continued to the smaller of two branches of the predecessor node (In this case the predecessor node is A179016(4)=7, for which hold both 7+A000120(8)=7+1=8 (the smaller branch) and 7+A000120(9)=7+2=9 (the larger branch). Thus the second term of this sequence is 5.

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

Complement of A213733. First differences: A218774.

Scheme
```
: (define (A213732 n) (1+ (A218772 n)))
```

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

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

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.

A218775 First differences of A218773.

Original entry on oeis.org

1, 2, 2, 1, 2, 1, 2, 2, 1, 3, 1, 1, 1, 2, 1, 3, 1, 1, 2, 1, 2, 4, 2, 1, 3, 1, 1, 2, 1, 2, 5, 1, 2, 1, 1, 1, 1, 1, 3, 1, 2, 1, 3, 1, 1, 2, 1, 2, 5, 1, 2, 1, 1, 1, 1, 1, 3, 2, 1, 2, 1, 1, 1, 1, 1, 4, 1, 1, 6, 1, 2, 2, 1, 3, 1, 1, 2, 1, 2, 5, 1, 2, 1, 1, 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 A213733. Cf. A218774, A218544, A218545.

(define (A218775 n) (- (A218773 (1+ n)) (A218773 n)))

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

cp's OEIS Frontend

A213732 Positions of even numbers greater than zero in A179016.

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

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A218775 First differences of A218773.

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