A228113 First differences of A057793.

5, 21, 142, 1059, 8360, 68940, 586140, 5096885, 45085903, 404203228, 3663001812, 33489858047, 308457620524, 2858876200536, 26639628764285, 249393770865090, 2344318815695001, 22116397127183516, 209317713015989446, 1986761935255798075, 18906449883376272709

Offset: 1

Author

Vladimir Pletser, Aug 10 2013

Keywords

• nonn

Comments

This sequence is an approximation to the number of primes with n digits (A006879). The error in the approximation is tabulated in A228114.

Because A057793(n) = Riemann(10^n) is not defined for n=0, we set its value to zero for our purpose of defining the differences.

Examples

			For n=1, A057793(1) - A057793(0) = 5 - 0 = 5.
		

References

• John H. Conway and R. K. Guy, "The Book of Numbers," Copernicus, an imprint of Springer-Verlag, NY, 1996, page 144-146.

Links

• Vladimir Pletser, Table of n, a(n) for n = 1..100 [a(40)-a(41) corrected by Sean A. Irvine]
• Eric Weisstein's World of Mathematics, Prime Counting Function.
• Eric Weisstein's World of Mathematics, Riemann Prime Counting Function.

Crossrefs

Cf. A006879, A057793, A228111, A228112, A228114, A228115, A228116.

Formula

a(n) = A057793(n) - A057793(n-1).