A175148 a(n) = number of primes p, p <= 2^n, where 2^n + p is composite.

0, 1, 1, 2, 3, 8, 13, 22, 43, 79, 140, 258, 480, 877, 1646, 3083, 5788, 10940, 20623, 39191, 74441, 141826, 270992, 518323, 993869, 1910174, 3674150, 7078905, 13654626, 26375091, 51007193, 98748888, 191381911, 371266503, 720861040, 1400887311, 2724578658, 5303077123, 10329261167, 20133043615

Offset

0,4

Comments

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

Links

Table of n, a(n) for n=0..39.

Formula

a(n) = A007053(n) - A175147(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 not isprime(t + p))
print([a(n) for n in range(20)]) # Michael S. Branicky, Feb 20 2023
(PARI) a(n) = {my(c = 0); forprime(p = 1, 2^n, if(!isprime(p + 2^n), c++)); c; } \\ Amiram Eldar, Jul 01 2025

Crossrefs

Cf. A007053, A175147.

Sequence in context: A376534 A142880 A147329 * A147417 A147357 A004138

Adjacent sequences: A175145 A175146 A175147 * A175149 A175150 A175151

Keyword

nonn

Author

Leroy Quet, Feb 24 2010

Extensions

a(19)-a(32) from Ray Chandler, Mar 05 2010

a(33)-a(39) from Amiram Eldar, Jul 01 2025

Status

approved