%I #17 Mar 30 2025 09:53:30

%S 0,2,54,23000,203280221,33483379603407,96601075195075186855

%N a(n) is the number of primes less than 4^(n^2).

%C Thue's proof, that there exist infinitely many primes, shows also that n+1 is a lower bound for a(n) (see Ribenboim, 2004).

%D Paulo Ribenboim, The Little Book of Bigger Primes, Springer-Verlag NY 2004. See pp. 9-10.

%H a(n) = pi(4^(n^2)).

%H a(n) = A007053(2*n^2). - _Amiram Eldar_, Mar 29 2025

%t a[n_]:=PrimePi[4^(n^2)]; Array[a,6,0]

%o (Python)

%o from sympy import primepi

%o def A382481(n): return primepi(1<<(n**2<<1)) # _Chai Wah Wu_, Mar 29 2025

%Y Cf. A000290, A000302, A000720, A007053, A060757.

%K nonn,hard,more

%O 0,2

%A _Stefano Spezia_, Mar 28 2025