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
Keywords
Examples
a(3) = pi(pi(pi(10^3))) = 12, the third entry in the table.
Links
- 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.
Programs
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Mathematica
f[n_] := Nest[PrimePi, 10^n, 3]; Table[ f[n], {n, 13}] (* Robert G. Wilson v, Dec 20 2004 *) -
PARI
nestpi(n,m) = { local(x,y,z); for(x=1,n,z=10^x;for(y=1,m,z=primepi(z));print1(z",")) }
Formula
a(n) = pi(pi(pi(10^n))) where pi(x) is the number of primes <= x.
Extensions
More terms from Robert G. Wilson v, Dec 20 2004
a(16)-a(24) from Robert G. Wilson v, Mar 11 2015