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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: A009658 A147794 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 September 28 09:11 EDT 2022. Contains 357068 sequences. (Running on oeis4.)