A327706 The minimal size of a partition lambda of n such that every partition of n with at most 6 parts can be obtained by coalescing the parts of lambda.

1, 2, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18, 18

Offset

1,2

Links

Table of n, a(n) for n=1..83.

Bo Jones and John Gunnar Carlsson, Minimum size generating partitions and their application to demand fulfillment optimization problems, arXiv:1909.09363 [math.CO], 2019.

Formula

Let L(n,k) be the analogous quantity if 6 is changed to k. Then L(n,k) = 1 + L(floor(n*(k-1)/k), k) with L(0,k) = 0.

Crossrefs

Cf. A327704 (k=4), A327705 (k=5), A327707 (k=7), A327708 (k=8).

Sequence in context: A091987 A357149 A025544 * A121856 A332061 A317442

Adjacent sequences: A327703 A327704 A327705 * A327707 A327708 A327709

Keyword

nonn

Author

Bo Jones, Oct 31 2019

Status

approved