A307990 Number of partitions of n into 2 distinct nonadjacent prime parts.

0, 0, 0, 0, 0, 0, 1, 0, 1, 1, 0, 0, 1, 1, 1, 2, 0, 1, 1, 2, 1, 2, 0, 2, 1, 2, 0, 2, 0, 2, 1, 2, 1, 3, 0, 3, 0, 1, 1, 3, 0, 3, 1, 3, 1, 3, 0, 5, 1, 4, 0, 2, 0, 5, 1, 3, 0, 3, 0, 5, 1, 2, 1, 5, 0, 6, 0, 1, 1, 5, 0, 6, 1, 4, 1, 5, 0, 6, 0, 4, 1, 4, 0, 7, 1, 4

Offset

1,16

Links

Table of n, a(n) for n=1..86.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{i=1..floor((n-1)/2)} (1-floor((pi(i)+1)/pi(n-i))) * A010051(i) * A010051(n-i), where pi is the prime counting function.

Example

a(7) = 1 since 7 = 2 + 5 is the only partition of 7 into two distinct nonadjacent prime parts.

Mathematica

Table[Sum[(1 - Floor[(PrimePi[i] + 1)/PrimePi[n - i]]) (PrimePi[i] - PrimePi[i - 1]) (PrimePi[n - i] - PrimePi[n - i - 1]), {i, Floor[(n - 1)/2]}], {n, 100}]

Crossrefs

Cf. A000720, A010051.

Cf. A307343.

Sequence in context: A060184 A055639 A156542 * A066360 A061358 A025866

Adjacent sequences: A307987 A307988 A307989 * A307991 A307992 A307993

Keyword

nonn,easy

Author

Wesley Ivan Hurt, May 09 2019

Status

approved