A100529 a(n) = minimal k such that n has a partition into k parts with the property that every number <= m can be partitioned into a subset of these parts.

1, 1, 1, 1, 2, 1, 1, 3, 4, 3, 4, 2, 2, 1, 1, 12, 15, 13, 14, 11, 12, 9, 10, 6, 6, 4, 4, 2, 2, 1, 1, 84, 91, 82, 89, 77, 80, 70, 73, 60, 63, 53, 54, 43, 44, 35, 36, 26, 26, 20, 20, 14, 14, 10, 10, 6, 6, 4, 4, 2, 2, 1, 1, 908

Offset

1,5

Links

Table of n, a(n) for n=1..64.

E. O'Shea, M-partitions: optimal partitions of weight for one scale pan, Discrete Math. 289 (2004), 81-93.

O. J. Rodseth, Enumeration of M-partitions, Discrete Math., 306 (2006), 694-698.

Formula

If 2^m + 2^(m-1) - 1 <= n <= 2^(m+1) - 1 for some m, let i = 2^(m+1) - 1 - n. Then a(n) = A000123([i/2]). This determines half the values.

Crossrefs

Cf. A000123 (binary partitions), A002033 (perfect partitions).

Sequence in context: A015138 A157807 A371279 * A262953 A226209 A302097

Adjacent sequences: A100526 A100527 A100528 * A100530 A100531 A100532

Keyword

nonn

Author

N. J. A. Sloane, Dec 31 2004

Status

approved