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%I #38 May 17 2021 14:58:29
%S 0,3,23,143,906,6116,44158,332774,2592592,20758029,169923159,
%T 1416705193,11992858452,102838308636,891604962452,7804289844393,
%U 68883734693928,612483070893536,5481624169369961,49347193044659702,446579871578168707,4060704006019620994,37083513766578631309,339996354713708049069,3128516637843038351228
%N Difference between pi(10^n) and the integer nearest to 10^n / log(10^n).
%D John H. Conway and R. K. Guy, "The Book of Numbers," Copernicus, an imprint of Springer-Verlag, NY, 1995, Page 146.
%H Eduard Roure Perdices, <a href="/A057835/b057835.txt">Table of n, a(n) for n = 1..28</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Prime_number_theorem">Prime number theorem</a>
%F a(n) = A006880(n) - A057834(n). - _Henry Bottomley_, Aug 10 2005
%F a(n) ~ 10^n/(n log 10)^2. - _Charles R Greathouse IV_, Mar 22 2015
%t Table[ PrimePi[10^n] - Round[ N[ 10^n/Log[ 10^n ] ] ], {n, 1, 13} ]
%o (PARI) a(n)=primepi(10^n)-round(10^n/log(10^n)) \\ _Charles R Greathouse IV_, Mar 22 2015
%K nonn
%O 1,2
%A _Robert G. Wilson v_, Nov 08 2000
%E More terms from _Jud McCranie_, Jun 21 2005
%E Corrected and extended by _Henry Bottomley_, Aug 10 2005
%E a(22) to a(25) from _Vladimir Pletser_, Aug 10 2013
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