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 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). 4
 0, 0, 0, -2, -8, 121, 2645, 27243, 209322, 1179803, 2299680, -61020043, -1269344630, -17189254160, -195686557968, -1996027658061, -18568445615842, -156279759410226, -1137747666182762, -6044328439309231, 1630706099481822, 705861452287757875 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS 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. LINKS Table of n, a(n) for n=1..22. Eric Weisstein's World of Mathematics, Prime Counting Function. Eric Weisstein's World of Mathematics, Fibonacci Polynomial. FORMULA a(n) = A006879(n) - A228063(n). CROSSREFS Cf. A006880, A006879, A228063, A228066, A228068. Sequence in context: A147794 A358152 A027530 * A271846 A009360 A202648 Adjacent sequences: A228061 A228062 A228063 * A228065 A228066 A228067 KEYWORD sign AUTHOR Vladimir Pletser, Aug 06 2013 STATUS approved

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Last modified June 24 16:36 EDT 2024. Contains 373680 sequences. (Running on oeis4.)