A096359 - OEIS

A096359

Numbers formed by the second nesting of pi(10^n).

2, 9, 39, 201, 1184, 7702, 53911, 397557, 3048955, 24106415, 195296943, 1613846646, 13556756261, 115465507935, 995112599484, 8663956207026, 76105984161825, 673776962356604, 6006525919368810, 53878729390812464, 485986685605473234, 4405654516157364292, 40121204955640303216, 366893555203205479291

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OFFSET

1,1

LINKS

Table of n, a(n) for n=1..24.

Jonathan Bayless, Dominic Klyve, and Tomás Oliveira e Silva, New Bounds and Computations on Prime-Indexed Primes, Integers, Vol.13, July 10, 2013.

FORMULA

Let pi(n) = the number of primes <= n. Then a(n) = pi(pi(n))

MATHEMATICA

Table[ Nest[ PrimePi, 10^n, 2], {n, 13}] (* Robert G. Wilson v, Jul 01 2004 *)

PROG

(PARI) nestpi(n, m) = { for(x=1, n, z=10^x; for(y=1, m, z=abs(primepi(z))); print1(floor(z)", ")) }