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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. 4
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 (list; graph; refs; listen; history; text; internal format)
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: A319516 A015138 A157807 * A262953 A226209 A302097

Adjacent sequences:  A100526 A100527 A100528 * A100530 A100531 A100532

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 31 2004

STATUS

approved

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Last modified June 20 05:01 EDT 2019. Contains 324229 sequences. (Running on oeis4.)