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

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

Offset

0,2

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

Links

Table of n, a(n) for n=0..6.

Formula

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

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

Example

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

Prog

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

Crossrefs

Cf. A000720, A001146, A007053.

Sequence in context: A122593 A267348 A264610 * A179389 A084123 A193473

Adjacent sequences: A153447 A153448 A153449 * A153451 A153452 A153453

Keyword

nonn,more

Author

Harry J. Smith, Dec 27 2008

Extensions

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

Status

approved