A228065 -id:A228065 - cp's OEIS frontend

A228066 a(n) = A006879(n) - A228065(n).

0, 3, 20, 120, 763, 5210, 38042, 288616, 2259818, 18165437, 149165130, 1246782034, 10576153259, 90845450184, 788766653816, 6912684881941, 61079444849535, 543599336199608, 4869141098476425, 43865568875289741, 397232678533509005, 3614124134441452287

Offset: 1

Vladimir Pletser, Aug 06 2013

Difference between the number of primes with n digits (A006879) and the difference of consecutive integers nearest to (10^n)/log(10^n) (see A228065).
The sequence A006879(n) is always > A228065(n) for 1 <= n <= 28.
The sequence (A228065) provides exactly the first value of pi(10^n)- pi(10^(n-1)) for n = 1, and yields an average relative difference in absolute value, i.e., average(abs(A228066(n))/(A006879(n))) = 0.0436296... for 1 <= n <= 28.
Note that A057834(n) = 10^n/log(10^n) is not defined for n = 0; its value is set arbitrarily to 0. - Updated by Eduard Roure Perdices, Apr 18 2021

Eduard Roure Perdices, Table of n, a(n) for n = 1..28
Eric Weisstein's World of Mathematics, Prime Counting Function

Cf. A006880, A006879, A228065.

a(n) = A006879(n) - A228065(n).

A228067 Difference of consecutive integers nearest to Li(10^n) - Li(2), where Li(x) = integral(0..x, dt/log(t)) (A190802, known as Gauss' approximation for the number of primes below 10^n).

Original entry on oeis.org

5, 24, 148, 1068, 8384, 68998, 586290, 5097291, 45087026, 404206380, 3663010786, 33489883880, 308457695529, 2858876419882, 26639629409596, 249393772773269, 2344318821362265, 22116397144079593, 209317713066531967, 1986761935407441102

Offset: 1

Vladimir Pletser, Aug 06 2013

nonn

This sequence gives a good approximation of the number of primes with n digits (A006879); see (A228068).

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

			For n = 1, A190802(1) - A190802(0) = 5-0 = 5.

Vladimir Pletser, Table of n, a(n) for n = 1..500
Eric Weisstein's World of Mathematics, Prime Counting Function
Eric Weisstein's World of Mathematics, Logarithmic Integral

Cf. A006879, A190802, A228068, A228065.

a(n) = A190802(n) - A190802(n-1).

cp's OEIS Frontend

A228066 a(n) = A006879(n) - A228065(n).

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