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

1,1

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.

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.

Formula

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

Example

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

Crossrefs

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

Sequence in context: A050910 A220378 A230645 * A306589 A221513 A284231

Adjacent sequences: A228110 A228111 A228112 * A228114 A228115 A228116

Keyword

nonn

Author

Vladimir Pletser, Aug 10 2013

Status

approved