A175147 a(n) = number of primes p, p <= 2^n, where 2^n + p is prime.

0, 0, 1, 2, 3, 3, 5, 9, 11, 18, 32, 51, 84, 151, 254, 429, 754, 1311, 2377, 4199, 7584, 13785, 24955, 45840, 84002, 153515, 283659, 524648, 976217, 1817659, 3392835, 6348677, 11898310

Offset

0,4

Comments

Terms through a(18) calculated by M. F. Hasler. Terms through a(29) calculated by Rick Shepherd.

Links

Table of n, a(n) for n=0..32.

Formula

a(n) = A007053(n) - A175148(n).

Prog

(Python)
from sympy import isprime, primerange
def a(n):
    t = 2**n
    return sum(1 for p in primerange(2, t+1) if isprime(t + p))
print([a(n) for n in range(20)]) # Michael S. Branicky, Feb 20 2023

Crossrefs

Cf. A007053, A175148.

Sequence in context: A296588 A065460 A241741 * A001180 A228778 A296674

Adjacent sequences: A175144 A175145 A175146 * A175148 A175149 A175150

Keyword

more,nonn

Author

Leroy Quet, Feb 24 2010

Extensions

a(30)-a(32) from Ray Chandler, Mar 05 2010

Status

approved