A327704 The minimal size of a partition lambda of n such that every partition of n with at most 4 parts can be obtained by coalescing the parts of lambda.

1, 2, 3, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14

Offset

1,2

Links

Table of n, a(n) for n=1..100.

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 4 is changed to k. Then L(n,k) = 1 + L(floor(n*(k-1)/k), k) with L(0,k) = 0.

Crossrefs

Cf. A327705 (k=5), A327706 (k=6), A327707 (k=7), A327708 (k=8).

Sequence in context: A329202 A318994 A261101 * A360924 A027434 A319434

Adjacent sequences: A327701 A327702 A327703 * A327705 A327706 A327707

Keyword

nonn

Author

Bo Jones, Sep 22 2019

Status

approved