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a(n) = prime(2^(2^n) + 1).
1

%I #20 Jul 28 2024 06:00:11

%S 5,11,59,1621,821647,104484802069,870566678511500413589

%N a(n) = prime(2^(2^n) + 1).

%C The k-th prime where k is the n-th Fermat number.

%H Andrew Booker, <a href="https://t5k.org/nthprime/index.php#n-th">The Nth Prime Page</a>.

%F From _Amiram Eldar_, Jul 11 2024: (Start)

%F a(n) = A000040(A000215(n)).

%F a(n) = A151800(A095124(n)). (End)

%e a(2) = prime(2^(2^2)+1) = prime(17) = 59.

%o (PARI) f(n) = for(x=1,n,print1(prime(2^2^x+1)","))

%Y Cf. A000040, A000215, A151800, A095124.

%K nonn,more

%O 0,1

%A _Cino Hilliard_, Jun 20 2004

%E a(5)-a(6) from _Amiram Eldar_, Jul 11 2024