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).

0, 0, 0, -2, -8, 121, 2645, 27243, 209322, 1179803, 2299680, -61020043, -1269344630, -17189254160, -195686557968, -1996027658061, -18568445615842, -156279759410226, -1137747666182762, -6044328439309231, 1630706099481822, 705861452287757875

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