A226983 a(n) = ceiling(n/2) - pi(2n) + pi(n-1).

0, -1, 0, 0, 1, 1, 1, 2, 2, 1, 2, 2, 3, 4, 4, 3, 4, 5, 5, 6, 6, 5, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 10, 9, 10, 9, 9, 10, 11, 10, 11, 11, 12, 13, 13, 13, 14, 15, 15, 15, 15, 14, 15, 15, 15, 15, 15, 15, 16, 17, 18, 19, 20, 19, 20, 19, 20, 21, 21, 20, 21, 22, 23, 24

Offset: 1

Author

Wesley Ivan Hurt, Jun 25 2013

Keywords

• sign
• easy

Comments

The number of partitions of 2n into exactly two parts such that the first part is an odd composite integer, n > 2.

Links

• Muniru A Asiru, Table of n, a(n) for n = 1..1000
• Index entries for sequences related to partitions

Crossrefs

Cf. A000720, A004526, A035250.

Programs

Maple

with(numtheory); seq(ceil(k/2)-(pi(2*k)-pi(k-1)),k=1..100);

Mathematica

Table[Floor[(n + 1) / 2] - (PrimePi[2 n] - PrimePi[n - 1]), {n, 100}] (* Vincenzo Librandi, Dec 07 2016 *)

PARI

a226983(n) = if(n==1, 0, ceil(n/2) - primepi(2*n) + primepi(n-1)) \\ Michael B. Porter, Jun 29 2013

Formula

a(n) = floor((n+1)/2) - ( pi(2n) - pi(n-1) ) = A004526(n+1) - A035250(n).