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

1,5

Links

Table of n, a(n) for n=1..74.

Index entries for sequences related to partitions

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).

Mathematica

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

Crossrefs

Cf. A010051, A062602.

Sequence in context: A029170 A079526 A353339 * A163822 A029203 A363526

Adjacent sequences: A291705 A291706 A291707 * A291709 A291710 A291711

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Oct 20 2017

Status

approved