cp's OEIS Frontend

A228064 Difference between the number of primes with n digits (A006879) and the nearest integer to F[4n](S(n)), where F[4n](x) are Fibonacci polynomials and S(n) = Sum_{i=0..3} (C(i)*(log(log(A*(B+n^2))))^i) (see A228063).

%I A228064 #14 Feb 16 2025 08:33:20
%S A228064 0,0,0,-2,-8,121,2645,27243,209322,1179803,2299680,-61020043,
%T A228064 -1269344630,-17189254160,-195686557968,-1996027658061,
%U A228064 -18568445615842,-156279759410226,-1137747666182762,-6044328439309231,1630706099481822,705861452287757875
%N A228064 Difference between the number of primes with n digits (A006879) and the nearest integer to F[4n](S(n)), where F[4n](x) are Fibonacci polynomials and S(n) = Sum_{i=0..3} (C(i)*(log(log(A*(B+n^2))))^i) (see A228063).
%C A228064 A228063 provides exactly the values of pi(10^n) - pi(10^(n-1)) for n = 1 to 3 and yields an average relative difference in absolute value, i.e., average(abs(A228064(n))/A006879(n) = 0.00473860... for 1 <= n <= 25, better than when using the 10^n/log(10^n) function, which yields 0.0469094... (see A228066) or the logarithmic integral (Li(10^n) - Li(2)) function, which yields 0.0175492... (see A228068) for 1 <= n <= 25.
%H A228064 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PrimeCountingFunction.html">Prime Counting Function</a>.
%H A228064 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/FibonacciPolynomial.html">Fibonacci Polynomial</a>.
%F A228064 a(n) = A006879(n) - A228063(n).
%Y A228064 Cf. A006880, A006879, A228063, A228066, A228068.
%K A228064 sign
%O A228064 1,4
%A A228064 _Vladimir Pletser_, Aug 06 2013