A228112 Difference between the number of primes with n digits (A006879) and the 6-parametric approximation of that number in A228111.

0, 0, 0, -2, -22, -23, 1614, 21952, 200754, 1427826, 6969680, -2536429, -648528610, -11247293516, -143493754330, -1578026921839, -15633412845816, -140582270611489, -1122913035234416, -7326349588043722, -25245049578998081, 301375487087871682, 9140885960557495580, 157255672291012140238, 2265259467069624459434

Offset

1,4

Comments

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.

Links

Table of n, a(n) for n=1..25.

Eric Weisstein's World of Mathematics, Prime Counting Function.

Eric Weisstein's World of Mathematics, Fibonacci Polynomial.

Formula

a(n) = A006879(n)- A228111(n).

Crossrefs

Cf. A006880, A006879, A228063, A228066, A228068, A228111, A228113, A228114, A228115, A228116.

Sequence in context: A284063 A153826 A080283 * A080433 A022373 A111751

Adjacent sequences: A228109 A228110 A228111 * A228113 A228114 A228115

Keyword

sign

Author

Vladimir Pletser, Aug 10 2013

Status

approved