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%I #15 Feb 24 2023 09:13:44
%S 0,0,0,-2,-22,-23,1614,21952,200754,1427826,6969680,-2536429,
%T -648528610,-11247293516,-143493754330,-1578026921839,-15633412845816,
%U -140582270611489,-1122913035234416,-7326349588043722,-25245049578998081,301375487087871682,9140885960557495580,157255672291012140238,2265259467069624459434
%N Difference between the number of primes with n digits (A006879) and the 6-parametric approximation of that number in A228111.
%C A228111 provides exact 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(A228112(n))/A006879(n) = 0.00375341... 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) or the Riemann (Riemann(10^n)) function, which yields 0.0103936... (see A228114) or the Fibonacci polynomials of multiple of 4 indices, which yields 0.00473860... (see A228064) for 1 <= n <= 25.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeCountingFunction.html">Prime Counting Function</a>.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/FibonacciPolynomial.html">Fibonacci Polynomial</a>.
%F a(n) = A006879(n)- A228111(n).
%Y Cf. A006880, A006879, A228063, A228066, A228068, A228111, A228113, A228114, A228115, A228116.
%K sign
%O 1,4
%A _Vladimir Pletser_, Aug 10 2013
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