A248371 Number of primes in Breusch's interval [n; 9(n+3)/8].

2, 2, 3, 2, 2, 2, 1, 2, 1, 2, 2, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 2, 2, 1, 1, 2, 2, 3, 3, 2, 3, 3, 3, 2, 2, 1, 2, 2, 2, 1, 1, 2, 2, 3, 3, 2, 2, 2, 3, 3, 3, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 4, 3, 3, 2, 2, 2, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2

Offset: 0

Author

M. F. Hasler, Oct 05 2014

Keywords

• nonn

Comments

Germán Andrés Paz proves that a(n) > 0 for all nonnegative n. - Charles R Greathouse IV, Jul 06 2020

Examples

			a(0)=a(1)=2 because in [0; 9(0+3)/8] = [0; 27/8] and in [1; 9(1+3)/8] = [1; 9/2] there are the two primes 2 and 3.
a(2)=3 because in [2; 9(2+3)/8] = [2; 45/8] there are the three primes 2, 3 and 5.
		

Links

• Jens Kruse Andersen, Table of n, a(n) for n = 0..10000
• Germán Andrés Paz, On the Interval [n; 2n]: Primes, Composites and Perfect Powers , Gen. Math. Notes 15 no. 1 (2013), 1-15.

Programs

Maple

with(numtheory): A248371:=n->pi(floor((n+3)*9/8))-pi(n-1): seq(A248371(n), n=0..100); # Wesley Ivan Hurt, Oct 05 2014

Mathematica

Table[PrimePi[(n + 3)*9/8] - PrimePi[n - 1], {n, 0, 100}] (* Wesley Ivan Hurt, Oct 05 2014 *)

PARI

a(n)=primepi((n+3)*9\8)-primepi(n-1)