A101226 Numbers formed by the fourth nesting of pi(10^n).

0, 2, 5, 14, 44, 165, 725, 3607, 19624, 115127, 716177, 4675144, 31743253, 222710685, 1606581461, 11868655658, 89506275569, 687275710608, 5361744667232, 42423406909091, 339921273158836, 2754682455861719, 22553369622588850, 186375668479844528

Offset: 1

Author

Cino Hilliard, Dec 15 2004

Keywords

• nonn

Examples

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

Links

• Kim Walisch, Fast C++ prime counting function implementation (primecount).

Crossrefs

Cf. A000720, A006880, A096359, A101225.

Programs

Mathematica

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

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)

Formula

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

a(n) = A000720(A101225(n)). - Amiram Eldar, Jun 29 2024

Extensions

a(10)-a(13) from Robert G. Wilson v, Dec 21 2004

a(14)-a(24) using Kim Walisch's primecount added by Amiram Eldar, Jun 29 2024