A308052 a(n) = nextprime(ceiling(n/2)-1), where nextprime(n) is the smallest prime > n.

2, 2, 2, 2, 3, 3, 5, 5, 5, 5, 7, 7, 7, 7, 11, 11, 11, 11, 11, 11, 11, 11, 13, 13, 13, 13, 17, 17, 17, 17, 17, 17, 17, 17, 19, 19, 19, 19, 23, 23, 23, 23, 23, 23, 23, 23, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 29, 31, 31, 31, 31, 37, 37, 37, 37, 37, 37

Offset

1,1

Comments

For n >= 3, a(n) is the smallest prime appearing among the larger parts of the partitions of n into two parts.

Links

Table of n, a(n) for n=1..68.

Index entries for sequences related to partitions

Formula

a(n) = A151800(ceiling(n/2)-1).

a(n) = A151800(floor((n-1)/2)). - Wesley Ivan Hurt, Jun 05 2021

Example

a(7) = 5; 7 has three partitions into two parts: (6,1), (5,2) and (4,3). The smallest prime among the larger parts is 5, so a(7) = 5.

Mathematica

Table[NextPrime[Ceiling[n/2] - 1, 1], {n, 100}]

Crossrefs

Cf. A151800.

Sequence in context: A081651 A269333 A029193 * A005858 A285798 A321346

Adjacent sequences: A308049 A308050 A308051 * A308053 A308054 A308055

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 10 2019

Status

approved