A361690 Number of primes in the interval [2^n, 2^n + n].

0, 2, 1, 1, 2, 1, 1, 1, 2, 1, 2, 1, 1, 0, 0, 3, 4, 0, 3, 0, 2, 1, 1, 3, 0, 0, 1, 0, 2, 1, 5, 1, 1, 2, 1, 0, 1, 2, 2, 2, 2, 1, 1, 2, 3, 0, 1, 3, 1, 0, 0, 1, 2, 2, 0, 3, 0, 2, 0, 0, 1, 3, 0, 1, 3, 0, 1, 2, 3, 1, 2, 2, 1, 1, 2, 3, 2, 4, 2, 2, 1, 2, 4, 1, 3, 0, 3, 2, 1, 2, 0

Offset: 0

Author

Jean-Marc Rebert, Mar 20 2023

Keywords

• nonn

Examples

			In the interval [2^1, 2^1 + 1] there are 2 primes (2 and 3). So a(1) = 2.
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A000720, A036378, A143537.

Programs

Maple

a:= n-> nops(select(isprime, [$2^n..2^n+n])):
seq(a(n), n=0..100);  # Alois P. Heinz, Mar 20 2023

Mathematica

Array[PrimePi[2^# + #] - PrimePi[2^# - 1] &, 50, 0] (* Michael De Vlieger, Mar 27 2023 *)

PARI

a(n)=#primes([2^n,2^n+n])

Python

from sympy import isprime
def A361690(n): return sum(1 for p in range((1<Chai Wah Wu, Mar 27 2023

Formula

From Alois P. Heinz, Mar 20 2023: (Start)

a(n) = pi(2^n+n) - pi(2^n-1), pi = A000720.

a(n) = A143537(2^n+n,2^n-1). (End)