A291564 Number of partitions of 2n into two parts such that one part is prime and the other is nonprime.

0, 1, 2, 2, 1, 3, 3, 2, 3, 4, 3, 3, 4, 5, 4, 7, 4, 3, 9, 6, 5, 8, 7, 5, 7, 9, 6, 10, 9, 5, 13, 8, 6, 15, 9, 8, 12, 11, 7, 14, 13, 7, 14, 15, 6, 16, 15, 10, 19, 13, 10, 17, 16, 12, 17, 15, 10, 18, 19, 6, 23, 20, 10, 25, 17, 14, 21, 22, 17, 20, 19, 12, 23, 24

Offset: 1

Author

Wesley Ivan Hurt, Oct 20 2017

Keywords

• nonn
• look
• easy

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A291563.

Programs

Maple

a:= n-> add(`if`(isprime(n+i) xor isprime(n-i), 1, 0), i=1..n-1):
seq(a(n), n=1..80);  # Alois P. Heinz, Mar 05 2021

Mathematica

Table[n - Sum[KroneckerDelta[(PrimePi[k] - PrimePi[k - 1]), (PrimePi[2 n - k] - PrimePi[2 n - 1 - k])], {k, n}], {n, 80}]

Formula

a(n) = n - Sum_{i=1..n} [A010051(i) = A010051(2n-i)], where [] is the Iverson bracket.

a(n) = n - A291563(n).