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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.

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A256443 Irregular triangle T(n,k) read by rows: row n gives a smallest partition of n with maximal order (see Comments for precise definition).

Original entry on oeis.org

1, 2, 3, 4, 2, 3, 6, 3, 4, 3, 5, 4, 5, 2, 3, 5, 5, 6, 3, 4, 5, 1, 3, 4, 5, 3, 4, 7, 3, 5, 7, 4, 5, 7, 2, 3, 5, 7, 5, 6, 7, 3, 4, 5, 7, 1, 3, 4, 5, 7, 2, 3, 4, 5, 7, 4, 5, 6, 7, 3, 5, 7, 8, 1, 3, 5, 7, 8, 4, 5, 7, 9, 1, 4, 5, 7, 9, 4, 5, 7, 11, 2, 3, 5, 7, 11
Offset: 1

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Author

Bob Selcoe, Mar 29 2015

Keywords

Comments

Consider all partitions of n for which the LCM of the parts is A000793(n) (A000793 is Landau's function g(n), the largest order of a permutation of n elements). Minimize the number of parts. Then take the lexicographically earliest solution. This is row n of the triangle. See A256445 for a partition with the most elements.

Examples

			Triangle starts T(1,1) = 1:
1:  1
2:  2
3:  3
4:  4
5:  2,3
6:  6
7:  3,4
8:  3,5
9:  4,5
10: 2,3,5
11: 5,6
12: 3,4,5
13: 1,3,4,5
14: 3,4,7
15: 3,5,7
16: 4,5,7
17: 2,3,5,7
18: 5,6,7
19: 3,4,5,7
20: 1,3,4,5,7
21: 2,3,4,5,7
22: 4,5,6,7
23: 3,5,7,8
T(11,k) = [5,6] rather than [1,2,3,5] because [5,6] has fewer elements.

Crossrefs

Cf. A000793, A074064, A256445.

Extensions

More terms from Alois P. Heinz, Apr 01 2015
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