A228114 Difference between the number of primes with n digits (A006879) and the difference of consecutive integers nearest to Riemann(10^n) (see A228113).

-1, 0, 1, 2, 3, -34, -59, -9, 176, 1749, 490, -842, 4297, 13427, -92418, -253834, 925307, 2903111, -27385699, 28776158, 81540379, 40700461, -1160432518, 2692289572, 175794995

Offset: 1

Author

Vladimir Pletser, Aug 10 2013

Keywords

• sign
• base
• less

Comments

The sequence (A228113) yields an average relative difference in absolute value, i.e. Average(Abs(A228114(n))/ (A006879(n)) = 1.03936…x10^-2 for 1<=n<=25.

Note that A057793(n) = Riemann(10^n) is not defined for n=0. Its value is set to 0.

Links

• Eric Weisstein's World of Mathematics, Prime Counting Function.
• Eric Weisstein's World of Mathematics, Riemann Prime Counting Function.

Crossrefs

Cf. A006880, A006879, A057793, A228111, A228112, A228113, A228115, A228116.

Formula

a(n) = A006879(n) - A228113(n).