A153450 Number of primes <= 2^(2^n) = pi(A001146(n)).

1, 2, 6, 54, 6542, 203280221, 425656284035217743

Offset: 0

Author

Harry J. Smith, Dec 27 2008

Keywords

• nonn
• more

Comments

The primes up to 2^(2^n) are exactly determined from the primes up to 2^(2^(n-1)), n >= 1, with the sieve of Eratosthenes. This gives an inductive algorithm to find all primes up to any integer (modulo space and time constraints...) This means that all odd primes are ultimately determined by the even prime, 2. - Daniel Forgues, Dec 04 2011

Examples

			a(3) = 54 because 2^(2^3) = 256 and there are 54 primes <= 256.
		

Crossrefs

Cf. A000720, A001146, A007053.

Programs

PARI

a(n)=primepi(1<<2^n) \\ Charles R Greathouse IV, Dec 05 2011

Formula

a(n) = pi(2^(2^n)) = A007053(2^n).

a(n) = A000720(A001146(n)).

Extensions

a(6) from Charles R Greathouse IV, Dec 05 2011