A327708 The minimal size of a partition lambda of n such that every partition of n with at most 8 parts can be obtained by coalescing the parts of lambda.

1, 2, 3, 4, 5, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 12, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 21, 21, 21, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22

Offset

1,2

Links

Table of n, a(n) for n=1..79.

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

Sequence in context: A102670 A289411 A328307 * A079631 A347623 A269849

Adjacent sequences: A327705 A327706 A327707 * A327709 A327710 A327711

Keyword

nonn

Author

Bo Jones, Oct 31 2019

Status

approved