A228114 - OEIS

%I #12 Feb 16 2025 08:33:20

%S -1,0,1,2,3,-34,-59,-9,176,1749,490,-842,4297,13427,-92418,-253834,

%T 925307,2903111,-27385699,28776158,81540379,40700461,-1160432518,

%U 2692289572,175794995

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

%C 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.

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

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeCountingFunction.html">Prime Counting Function</a>.

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/RiemannPrimeCountingFunction.html">Riemann Prime Counting Function</a>.

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

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

%K sign,base,less

%O 1,4

%A _Vladimir Pletser_, Aug 10 2013