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The minimal size of a partition lambda of n such that every partition of n with at most 5 parts can be obtained by coalescing the parts of lambda.
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%I #17 Feb 24 2020 16:40:21

%S 1,2,3,4,5,5,6,6,7,7,7,8,8,8,9,9,9,9,10,10,10,10,10,11,11,11,11,11,11,

%T 12,12,12,12,12,12,12,12,13,13,13,13,13,13,13,13,13,13,14,14,14,14,14,

%U 14,14,14,14,14,14,14,15,15,15,15,15,15,15,15,15,15,15,15,15,15,15,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,17,17,17,17,17,17,17

%N The minimal size of a partition lambda of n such that every partition of n with at most 5 parts can be obtained by coalescing the parts of lambda.

%H Bo Jones and John Gunnar Carlsson, <a href="https://arxiv.org/abs/1909.09363">Minimum size generating partitions and their application to demand fulfillment optimization problems</a>, arXiv:1909.09363 [math.CO], 2019.

%F Let L(n,k) be the analogous quantity if 5 is changed to k. Then L(n,k) = 1 + L(floor(n*(k-1)/k), k) with L(0,k) = 0.

%Y Cf. A327704 (k=4), A327706 (k=6), A327707 (k=7), A327708 (k=8).

%K nonn

%O 1,2

%A _Bo Jones_, Sep 22 2019