A327705 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.

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, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 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

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

Sequence in context: A293771 A005245 A061373 * A104135 A354535 A276656

Adjacent sequences: A327702 A327703 A327704 * A327706 A327707 A327708

Keyword

nonn

Author

Bo Jones, Sep 22 2019

Status

approved