%I #16 Jun 29 2024 07:16:50

%S 0,2,5,14,44,165,725,3607,19624,115127,716177,4675144,31743253,

%T 222710685,1606581461,11868655658,89506275569,687275710608,

%U 5361744667232,42423406909091,339921273158836,2754682455861719,22553369622588850,186375668479844528

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

%H Kim Walisch, <a href="https://github.com/kimwalisch/primecount">Fast C++ prime counting function implementation (primecount)</a>.

%F a(n) = pi(pi(pi(pi(10^n)))) where pi(x) is the number of primes <= x.

%F a(n) = A000720(A101225(n)). - _Amiram Eldar_, Jun 29 2024

%e a(3) = pi(pi(pi(pi(10^3)))) = 5, the third entry in the table.

%t f[n_] := Nest[PrimePi, 10^n, 4]; Table[ f[n], {n, 13}] (* _Robert G. Wilson v_, Dec 21 2004 *)

%o (PARI) nestpi(n,m) = { my(x,y,z); for(x=1, n, z=10^x; for(y=1, m, z=primepi(z)); print1(z", ")) } \\ try call nestpi(11, 4)

%Y Cf. A000720, A006880, A096359, A101225.

%K nonn

%O 1,2

%A _Cino Hilliard_, Dec 15 2004

%E a(10)-a(13) from _Robert G. Wilson v_, Dec 21 2004

%E a(14)-a(24) using Kim Walisch's primecount added by _Amiram Eldar_, Jun 29 2024