A101225 Numbers formed by the third nesting of pi(10^n).

1, 4, 12, 46, 194, 977, 5492, 33666, 220068, 1513371, 10833076, 80104927, 608455060, 4726881850, 37431015268, 301327263751, 2460711566651, 20348625806080, 170149286304116, 1436870802519360, 12241980697771924, 105136072207222852, 909475787902559408, 7919305232077304848

Offset

1,2

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, Electronic J. of Combinatorial Number Theory, Vol. 13, Paper A43, 2013.

Formula

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

Example

a(3) = pi(pi(pi(10^3))) = 12, the third entry in the table.

Mathematica

f[n_] := Nest[PrimePi, 10^n, 3]; Table[ f[n], {n, 13}] (* Robert G. Wilson v, Dec 20 2004 *)

Prog

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

Crossrefs

Cf. A006880, A096359.

Sequence in context: A149373 A259203 A151464 * A000775 A149374 A149375

Adjacent sequences: A101222 A101223 A101224 * A101226 A101227 A101228

Keyword

nonn

Author

Cino Hilliard, Dec 15 2004

Extensions

More terms from Robert G. Wilson v, Dec 20 2004

a(16)-a(24) from Robert G. Wilson v, Mar 11 2015

Status

approved