A291563 Number of partitions of 2n into two prime parts or two nonprime parts.

1, 1, 1, 2, 4, 3, 4, 6, 6, 6, 8, 9, 9, 9, 11, 9, 13, 15, 10, 14, 16, 14, 16, 19, 18, 17, 21, 18, 20, 25, 18, 24, 27, 19, 26, 28, 25, 27, 32, 26, 28, 35, 29, 29, 39, 30, 32, 38, 30, 37, 41, 35, 37, 42, 38, 41, 47, 40, 40, 54, 38, 42, 53, 39, 48, 52, 46, 46

Offset: 1

Author

Wesley Ivan Hurt, Oct 20 2017

Keywords

• nonn
• easy

Links

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

Crossrefs

Cf. A010051, A291564.

Programs

Maple

a:= n-> 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[Sum[KroneckerDelta[(PrimePi[k] - PrimePi[k - 1]), (PrimePi[2 n - k] - PrimePi[2 n - 1 - k])], {k, n}], {n, 80}]

Formula

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

a(n) = n - A291564(n).