A228068 Difference between the number of primes with n digits (A006879) and the difference of consecutive integers nearest to Li(10^n) - Li(2) (see A228067).

-1, -3, -5, -7, -21, -92, -209, -415, -947, -1403, -8484, -26675, -70708, -205919, -737729, -2162013, -4741957, -13992966, -77928220, -122866869, -374649610, -1334960954, -5317831008, -9896721062, -38014073661

Offset: 1

Author

Vladimir Pletser, Aug 06 2013

Keywords

• sign

Comments

The sequence A006879(n) is always < A228067(n) for 1 <= n <= 25.

The sequence (A228067) yields an average relative difference in absolute value, i.e., average(abs(A228068(n))/A006879(n) = 0.0175492... for 1 <= n <= 25.

Note that A190802(n) = (Li(10^n) - Li(2)) is not defined for n=0. Its value is set arbitrarily to 0.

Links

• Eric Weisstein's World of Mathematics, Prime Counting Function
• Eric Weisstein's World of Mathematics, Logarithmic Integral

Crossrefs

Cf. A006880, A006879, A228067, A228066.

Formula

a(n) = A006879(n) - A228067(n).