A294602 a(n) = pi(n-1) - pi(floor(n/2)), where pi is A000720.

0, 0, 1, 1, 1, 1, 1, 2, 2, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 4, 4, 3, 3, 4, 4, 3, 3, 3, 3, 4, 4, 5, 5, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 6, 6, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 9, 9, 10, 10, 9

Offset: 1

Author

Arkadiusz Wesolowski, Nov 03 2017

Keywords

• nonn
• easy

Comments

Number of primes in the interval (n/2, n).

Number of primes among the larger parts of the partitions of n into two distinct parts. For n=8, the partitions of 8 into two distinct parts are (7,1), (6,2), (5,3); 7 and 5 are prime so a(8) = 2. - Wesley Ivan Hurt, Apr 07 2018

Examples

			a(8) = 2 because there are 2 primes between 4 and 8: 5, 7.
a(19) = 3 because there are 3 primes between 9 and 19: 11, 13, 17.
		

Crossrefs

Cf. A000720, A001221, A010051, A056171.

Programs

Magma

[0, 0] cat [#PrimesInInterval(Floor(n/2)+1, n-1): n in [3..86]];

Maple

A294602 := proc(n)
    numtheory[pi](n-1)-numtheory[pi](floor(n/2)) ;
end proc:
seq(A294602(n),n=1..120) ; # R. J. Mathar, Dec 17 2017

Mathematica

Array[PrimePi[# - 1] - PrimePi[Floor[#/2]] &, 86] (* Michael De Vlieger, Nov 03 2017 *)

PARI

vector(86, n, primepi(n-1)-primepi(n\2))

Formula

a(n) = A056171(n) - A010051(n).

a(n) = Sum_{i=1..floor((n-1)/2)} A010051(n-i). - Wesley Ivan Hurt, Apr 07 2018