%I A100529
%S A100529 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,
%T A100529 1,84,91,82,89,77,80,70,73,60,63,53,54,43,44,35,36,26,26,20,20,14,
%U A100529 14,10,10,6,6,4,4,2,2,1,1,908
%N 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.
%D A100529 E. O'Shea, M-partitions: optimal partitions of weight for one scale pan, 
               Discrete Math 289 (2004), 81-93.
%D A100529 O. J. Rodseth, Enumeration of M-partitions, Discrete Math., 306 (2006), 
               694-698.
%F A100529 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.
%Y A100529 Cf. A000123 (binary partitions), A002033 (perfect partitions).
%Y A100529 Sequence in context: A055068 A015138 A157807 this_sequence A124424 A057044 
               A153899
%Y A100529 Adjacent sequences: A100526 A100527 A100528 this_sequence A100530 A100531 
               A100532
%K A100529 nonn
%O A100529 1,5
%A A100529 N. J. A. Sloane (njas(AT)research.att.com), Dec 31 2004