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

Author

N. J. A. Sloane, Dec 31 2004

Keywords

• nonn

Links

• 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.

Crossrefs

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

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.