A347788 Number of compositions (ordered partitions) of n into at most 2 nonprime parts.

1, 1, 1, 0, 1, 2, 1, 2, 2, 3, 5, 2, 4, 4, 5, 5, 8, 4, 8, 6, 8, 7, 11, 6, 12, 9, 13, 9, 14, 10, 16, 12, 14, 13, 19, 13, 22, 14, 17, 17, 22, 16, 24, 18, 22, 19, 25, 18, 28, 21, 28, 21, 28, 22, 32, 25, 30, 25, 33, 26, 38, 28, 31, 29, 38, 29, 42, 30, 34, 33, 42

Offset: 0

Author

Ilya Gutkovskiy, Sep 13 2021

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 0..10000

Crossrefs

Cf. A005171, A018252, A052284, A076608, A347796, A347797, A347798, A347799, A358638.

Programs

Mathematica

Table[Length@Flatten[Permutations/@IntegerPartitions[n,2,Select[Range@n,!PrimeQ@#&]],1],{n,0,70}] (* Giorgos Kalogeropoulos, Sep 13 2021 *)

PARI

A347788(n) = if(n<2,1,!isprime(n)+sum(k=1,n-1,!(isprime(k)+isprime(n-k)))); \\ Antti Karttunen, Nov 25 2022