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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
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
Sequence in context: A147794 A358152 A027530 * A271846 A009360 A202648
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.)