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

1,8

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

Links

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

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

Example

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.

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 *)

Prog

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

Crossrefs

Cf. A000720, A001221, A010051, A056171.

Sequence in context: A198337 A206483 A087011 * A000174 A156268 A053257

Adjacent sequences: A294599 A294600 A294601 * A294603 A294604 A294605

Keyword

nonn,easy

Author

Arkadiusz Wesolowski, Nov 03 2017

Status

approved