cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A213733 Positions of odd numbers in A179016.

Original entry on oeis.org

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

Views

Author

Antti Karttunen, Nov 01 2012

Keywords

Comments

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.

Examples

			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.

Links

Crossrefs

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

Programs

Formula

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

Extensions

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

A218773 Positions in the infinite trunk of beanstalk (see A179016) where the next node upwards is the larger of the two possible branches.

Original entry on oeis.org

0, 1, 3, 5, 6, 8, 9, 11, 13, 14, 17, 18, 19, 20, 22, 23, 26, 27, 28, 30, 31, 33, 37, 39, 40, 43, 44, 45, 47, 48, 50, 55, 56, 58, 59, 60, 61, 62, 63, 66, 67, 69, 70, 73, 74, 75, 77, 78, 80, 85, 86, 88, 89, 90, 91, 92, 93, 96, 98, 99, 101, 102, 103, 104, 105, 106
Offset: 1

Views

Author

Antti Karttunen, Nov 05 2012

Keywords

Examples

			A179016(0) = 0 is the first case where the next term A179016(2) = 1 is the larger of two branches from 0 (the smaller branch in this case being 0 itself, as 0 = 0+A000120(0)), thus the first term of this sequence is 0.
A179016(1) = 1 is the second case where the next term A179016(3) = 3 is the larger of two branches from 1 (the smaller branch in this case being 2, as 2 = 1+A000120(2), 2 being a leaf node, one of the terms of A055938), thus the second term of this sequence is 1.

Links

Crossrefs

Characteristic function: A213729 shifted once left. Complement: A218772. a(n) = A213733(n)-1. First differences: A218775.

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

Views

Author

Antti Karttunen, Nov 05 2012

Keywords

Links

Crossrefs

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

Programs

Formula

a(n) = A218772(n+1)-A218772(n).
Showing 1-3 of 3 results.

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