A175147 - OEIS

%I #12 Feb 20 2023 14:49:36

%S 0,0,1,2,3,3,5,9,11,18,32,51,84,151,254,429,754,1311,2377,4199,7584,

%T 13785,24955,45840,84002,153515,283659,524648,976217,1817659,3392835,

%U 6348677,11898310

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

%C Terms through a(18) calculated by _M. F. Hasler_. Terms through a(29) calculated by Rick Shepherd.

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

%o (Python)

%o from sympy import isprime, primerange

%o def a(n):

%o     t = 2**n

%o     return sum(1 for p in primerange(2, t+1) if isprime(t + p))

%o print([a(n) for n in range(20)]) # _Michael S. Branicky_, Feb 20 2023

%Y Cf. A007053, A175148.

%K more,nonn

%O 0,4

%A _Leroy Quet_, Feb 24 2010

%E a(30)-a(32) from _Ray Chandler_, Mar 05 2010