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

0,2

Links

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

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)

Example

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

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 *)

Prog

(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<<n)+1, (1<<n)+n+1, 2) if isprime(p)) if n != 1 else 2 # Chai Wah Wu, Mar 27 2023

Crossrefs

Cf. A000720, A036378, A143537.

Sequence in context: A056731 A042974 A235757 * A020906 A220280 A355242

Adjacent sequences: A361687 A361688 A361689 * A361691 A361692 A361693

Keyword

nonn

Author

Jean-Marc Rebert, Mar 20 2023

Status

approved