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).

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

Vladimir Pletser, Table of n, a(n) for n = 1..500

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

Cf. A006879, A190802, A228068, A228065.

Sequence in context: A221788 A111766 A368534 * A372138 A322208 A241134

Adjacent sequences: A228064 A228065 A228066 * A228068 A228069 A228070

Keyword

nonn

Author

Vladimir Pletser, Aug 06 2013

Status

approved