A302480 Number of partitions of n into two parts with the smaller part nonprime and the larger part prime.

0, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 1, 1, 1, 1, 0, 2, 1, 2, 2, 3, 1, 3, 1, 3, 1, 3, 1, 3, 1, 3, 3, 4, 1, 4, 0, 4, 3, 3, 1, 4, 1, 4, 3, 5, 2, 5, 1, 5, 2, 6, 3, 6, 2, 6, 4, 7, 3, 6, 1, 6, 5, 6, 2, 7, 1, 7, 6, 7, 3, 8, 3, 8, 5, 8, 4, 9, 2, 9, 6, 9, 5, 9, 2, 9, 5

Offset

1,17

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/2)} (1 - A010051(i)) * A010051(n-i).

Example

a(17) = 2; 17 = 13+4 = 11+6, smaller parts are nonprimes larger are prime.

Mathematica

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

Prog

(PARI) a(n) = sum(i=1, n\2, (1-isprime(i))*isprime(n-i)); \\ Michel Marcus, Apr 09 2018

Crossrefs

Cf. A010051, A302481.

Sequence in context: A210868 A176853 A261787 * A329656 A000374 A355735

Adjacent sequences: A302477 A302478 A302479 * A302481 A302482 A302483

Keyword

nonn,easy

Author

Wesley Ivan Hurt, Apr 08 2018

Status

approved