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A228066
a(n) = A006879(n) - A228065(n).
6
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
KEYWORD
nonn,base,less
AUTHOR
Vladimir Pletser, Aug 06 2013
STATUS
approved