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A228067
Difference of consecutive integers nearest to Li(10^n) - Li(2), where Li(x) = integral(0..x, dt/log(t)) (A190802, known as Gauss' approximation for the number of primes below 10^n).
2
5, 24, 148, 1068, 8384, 68998, 586290, 5097291, 45087026, 404206380, 3663010786, 33489883880, 308457695529, 2858876419882, 26639629409596, 249393772773269, 2344318821362265, 22116397144079593, 209317713066531967, 1986761935407441102
OFFSET
1,1
COMMENTS
This sequence gives a good approximation of the number of primes with n digits (A006879); see (A228068).
Note that A190802(n)=(Li(10^n)-Li(2)) is not defined for n=0. Its value is arbitrarily set to 0.
LINKS
Eric Weisstein's World of Mathematics, Prime Counting Function
Eric Weisstein's World of Mathematics, Logarithmic Integral
FORMULA
a(n) = A190802(n) - A190802(n-1).
EXAMPLE
For n = 1, A190802(1) - A190802(0) = 5-0 = 5.
CROSSREFS
KEYWORD
nonn
AUTHOR
Vladimir Pletser, Aug 06 2013
STATUS
approved