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A228066 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). 6
0, 3, 20, 120, 763, 5210, 38042, 288616, 2259818, 18165437, 149165130, 1246782034, 10576153259, 90845450184, 788766653816, 6912684881941, 61079444849535, 543599336199608, 4869141098476425, 43865568875289741, 397232678533509005, 3614124134441452287 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The sequence A006879(n) is always > A228065(n) for 1<=n<=25.

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. <ARD(A228066)> = Average(Abs(A228066(n))/ (A006879(n)) = 4.69094…x10^-2 for 1<=n<=25.

Note that A057834(n)=(10^n)/log(10^n) is not defined for n=0. Its value is set arbitrarily to 0.

LINKS

Table of n, a(n) for n=1..22.

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

AUTHOR

Vladimir Pletser, Aug 06 2013

STATUS

approved

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Last modified September 22 10:23 EDT 2020. Contains 337289 sequences. (Running on oeis4.)