A308050 a(n) = n - prevprime(n - 1), where prevprime(n) is the largest prime < n.

2, 2, 3, 2, 3, 2, 3, 4, 5, 2, 3, 2, 3, 4, 5, 2, 3, 2, 3, 4, 5, 2, 3, 4, 5, 6, 7, 2, 3, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 2, 3, 2, 3, 4, 5, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 6, 7, 2, 3, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 2, 3, 2, 3, 4, 5, 6, 7, 2, 3, 4, 5, 2, 3, 4, 5, 6

Offset

4,1

Comments

a(n) is the smallest part appearing in the single partition of n into two parts whose largest prime part is < n - 1.

Links

Table of n, a(n) for n=4..89.

Index entries for sequences related to partitions

Formula

a(n) = n - A151799(n - 1).

Example

a(11) = 4; 11 has 5 partitions into 2 parts: (10,1), (9,2), (8,3), (7,4) and (6,5). The single partition containing the largest prime part < 10 is (7,4) and 4 is the smallest part in this partition, so a(11) = 4.

Mathematica

Table[n - NextPrime[n - 1, -1], {n, 4, 100}]

Crossrefs

Cf. A151799.

Sequence in context: A295568 A099427 A059964 * A248147 A087458 A052180

Adjacent sequences: A308047 A308048 A308049 * A308051 A308052 A308053

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 10 2019

Status

approved