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

1,2

Comments

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

Links

Eduard Roure Perdices, Table of n, a(n) for n = 1..28

Eric Weisstein's World of Mathematics, Prime Counting Function

Formula

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

Crossrefs

Cf. A006880, A006879, A228065.

Sequence in context: A128910 A037788 A037669 * A009125 A037795 A325890

Adjacent sequences: A228063 A228064 A228065 * A228067 A228068 A228069

Keyword

nonn,base,less

Author

Vladimir Pletser, Aug 06 2013

Status

approved