%I #8 May 31 2018 11:22:34
%S 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,
%T 84,91,82,89,77,80,70,73,60,63,53,54,43,44,35,36,26,26,20,20,14,14,10,
%U 10,6,6,4,4,2,2,1,1,908
%N 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.
%H E. O'Shea, <a href="https://dx.doi.org/10.1016/j.disc.2004.07.016">M-partitions: optimal partitions of weight for one scale pan</a>, Discrete Math. 289 (2004), 81-93.
%H O. J. Rodseth, <a href="https://dx.doi.org/10.1016/j.disc.2006.02.010">Enumeration of M-partitions</a>, Discrete Math., 306 (2006), 694-698.
%F 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 Cf. A000123 (binary partitions), A002033 (perfect partitions).
%K nonn
%O 1,5
%A _N. J. A. Sloane_, Dec 31 2004