A291708 Number of partitions of n into two prime parts or two nonprime parts.

0, 1, 0, 1, 2, 1, 2, 2, 2, 4, 1, 3, 3, 4, 3, 6, 2, 6, 4, 6, 4, 8, 3, 9, 5, 9, 4, 9, 5, 11, 7, 9, 7, 13, 6, 15, 7, 10, 9, 14, 8, 16, 10, 14, 10, 16, 9, 19, 11, 18, 10, 17, 11, 21, 13, 18, 12, 20, 13, 25, 15, 18, 15, 24, 14, 27, 15, 19, 17, 26, 16, 28, 18, 25

Offset: 1

Author

Wesley Ivan Hurt, Oct 20 2017

Keywords

• nonn
• easy

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A062602.

Programs

Mathematica

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

Formula

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

a(n) = floor(n/2) - A062602(n).