A335186 a(n) = nextprime(ceiling(n/2)-1) + prevprime(floor(n/2)+1), where nextprime = A151800 and prevprime = A151799.

4, 5, 6, 8, 8, 8, 10, 12, 12, 12, 14, 18, 18, 18, 18, 18, 18, 18, 22, 24, 24, 24, 26, 30, 30, 30, 30, 30, 30, 30, 34, 36, 36, 36, 38, 42, 42, 42, 42, 42, 42, 42, 46, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 52, 58, 60, 60, 60, 62, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 68, 74

Offset

4,1

Comments

a(n) is the sum of the smallest prime appearing among the largest parts of the partitions of n into two parts and the largest prime appearing among the smallest parts of the partitions of n into two parts.

If n = 2p where p is prime, then a(n) = n. The converse is not true since a(8) = 8, but n = 2*4 and 4 is not prime.

All terms are even except a(5).

Links

Table of n, a(n) for n=4..74.

Index entries for sequences related to partitions

Formula

a(n) = A151800(ceiling(n/2)-1) + A151799(floor(n/2)+1).

Example

a(5) = 5; n=5 has 2 partitions into two parts: (4,1) and (3,2). Among the largest parts, the smallest prime is 3. Among the smallest parts, 2 is the largest. So a(5) = 3 + 2 = 5.
a(6) = 6; n=6 has 3 partitions into two parts: (5,1), (4,2) and (3,3). Among the largest parts, the smallest prime is 3. Among the smallest parts, the largest prime is 3. So a(6) = 3 + 3 = 6.
a(7) = 8; n=7 has 3 partitions into two parts: (6,1), (5,2) and (4,3). Among the largest parts, 5 is the smallest. Among the smallest parts, 3 is the largest. So a(7) = 5 + 3 = 8.

Mathematica

Table[NextPrime[Ceiling[n/2] - 1, 1] + NextPrime[Floor[n/2] + 1, -1], {n, 4, 100}]

Prog

(Magma) [NextPrime(Ceiling(n/2)-1) + PreviousPrime(Floor(n/2)+1) : n in [4..100]];

Crossrefs

Cf. A001223 (prime gaps), A151799, A151800, A335185.

Sequence in context: A051036 A063673 A105737 * A257816 A033597 A336379

Adjacent sequences: A335183 A335184 A335185 * A335187 A335188 A335189

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 25 2020

Status

approved