A374151 The number of prime-indexed primes below 2^n.

0, 0, 1, 2, 3, 5, 7, 11, 16, 25, 39, 63, 103, 172, 290, 490, 844, 1464, 2564, 4522, 8022, 14325, 25686, 46382, 84115, 153327, 280423, 514798, 948374, 1752639, 3248574, 6037968, 11250482, 21013808, 39336188, 73788697, 138689231, 261150360, 492602752, 930716294

Offset: 0

Author

Amiram Eldar, Jun 29 2024

Keywords

• nonn

Comments

The data was calculated using Kim Walisch's primecount program.

Examples

			a(1) = 0 since primepi(primepi(2^1)) = primepi(primepi(2)) = primepi(1) = 0.
a(2) = 1 since primepi(primepi(2^2)) = primepi(primepi(4)) = primepi(2) = 1.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..77
• Kim Walisch, Fast C++ prime counting function implementation (primecount).
• Wikipedia, Super-prime.

Crossrefs

Cf. A000720, A006450, A007053, A096359, A374150.

Programs

Mathematica

Table[PrimePi[PrimePi[2^n]], {n, 0, 40}]

PARI

a(n) = primepi(primepi(2^n));

Formula

a(n) = A000720(A007053(n)).

a(n) = A132090(2^n).