A153450 - OEIS

%I #27 Nov 26 2023 17:51:55

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

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

%C 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

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

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

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

%o (PARI) a(n)=primepi(1<<2^n) \\ _Charles R Greathouse IV_, Dec 05 2011

%Y Cf. A000720, A001146.

%K nonn,more

%O 0,2

%A _Harry J. Smith_, Dec 27 2008

%E a(6) from _Charles R Greathouse IV_, Dec 05 2011