A360635 a(n) is the smallest nonnegative integer that satisfies p(a(n)+1) - p(a(n)) >= n, where p denotes the number partition function.

0, 1, 3, 5, 5, 7, 7, 7, 8, 9, 9, 9, 9, 10, 10, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 13, 13, 13, 13, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 14, 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, 17, 17

Offset

0,3

Comments

Conjecture: except for the values 2, 4 and 6, this sequence includes all the nonnegative integers.

Links

Table of n, a(n) for n=0..68.

Christoph Koutschan, Ali K. Uncu, and Elaine Wong, A Unified Approach to Unimodality of Gaussian Polynomials, arXiv:2302.04067 [cs.SC], 2023.

Mathematica

a={}; For[n=0, n<=68, n++, k=0; While[PartitionsP[k+1]-PartitionsP[k]<n, k++]; AppendTo[a, k]]; a

Prog

(PARI) a(n) = my(k=0); while (numbpart(k+1) - numbpart(k) < n, k++); k; \\ Michel Marcus, Feb 15 2023

Crossrefs

Cf. A000041, A001477, A187219.

Sequence in context: A175767 A111800 A190136 * A126611 A164019 A307701

Adjacent sequences: A360632 A360633 A360634 * A360636 A360637 A360638

Keyword

nonn

Author

Stefano Spezia, Feb 14 2023

Status

approved