A096359 - OEIS

%I #22 Mar 11 2015 09:49:32

%S 2,9,39,201,1184,7702,53911,397557,3048955,24106415,195296943,

%T 1613846646,13556756261,115465507935,995112599484,8663956207026,

%U 76105984161825,673776962356604,6006525919368810,53878729390812464,485986685605473234,4405654516157364292,40121204955640303216,366893555203205479291

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

%H Jonathan Bayless, Dominic Klyve, and Tomás Oliveira e Silva, <a href="http://www.emis.de/journals/INTEGERS/papers/n43/n43.Abstract.html">New Bounds and Computations on Prime-Indexed Primes</a>, Integers, Vol.13, July 10, 2013.

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

%t Table[ Nest[ PrimePi, 10^n, 2], {n, 13}] (* _Robert G. Wilson v_, Jul 01 2004 *)

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

%Y Cf. A006880, A101225, A101226.

%K nonn

%O 1,1

%A _Cino Hilliard_, Jun 30 2004

%E a(10) - a(15) from _Robert G. Wilson v_, Jul 01 2004

%E a(16) - a(19) from _Henri Lifchitz_, Nov 11 2012

%E a(20) - a(24) from Bayless, Table 1, p.7, _Jonathan Vos Post_, Aug 09 2013