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%I #7 Jun 29 2024 10:58:38
%S 0,0,1,2,3,5,7,11,16,25,39,63,103,172,290,490,844,1464,2564,4522,8022,
%T 14325,25686,46382,84115,153327,280423,514798,948374,1752639,3248574,
%U 6037968,11250482,21013808,39336188,73788697,138689231,261150360,492602752,930716294
%N The number of prime-indexed primes below 2^n.
%C The data was calculated using Kim Walisch's primecount program.
%H Amiram Eldar, <a href="/A374151/b374151.txt">Table of n, a(n) for n = 0..77</a>
%H Kim Walisch, <a href="https://github.com/kimwalisch/primecount">Fast C++ prime counting function implementation (primecount)</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Super-prime">Super-prime</a>.
%F a(n) = A000720(A007053(n)).
%F a(n) = A132090(2^n).
%e a(1) = 0 since primepi(primepi(2^1)) = primepi(primepi(2)) = primepi(1) = 0.
%e a(2) = 1 since primepi(primepi(2^2)) = primepi(primepi(4)) = primepi(2) = 1.
%t Table[PrimePi[PrimePi[2^n]], {n, 0, 40}]
%o (PARI) a(n) = primepi(primepi(2^n));
%Y Cf. A000720, A006450, A007053, A096359, A374150.
%K nonn
%O 0,4
%A _Amiram Eldar_, Jun 29 2024