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%I #35 Sep 08 2022 08:45:58
%S 7,27,169,1217,9512,78030,661458,5740303,50701542,454011971,
%T 4110416300,37550193649,345618860220,3201414635780,29816233849000,
%U 279007258230819,2621647966812031,24723998785919976,233922961602470390,2219671974013732243
%N Floor((10^n)/(log(10^n) - 1)).
%C lim n -> infinity (log(n) - n/pi(n)) = 1, where pi(n) is the prime counting function.
%D A. M. Legendre, Essai sur la Théorie des Nombres, Paris: Duprat, 1808.
%H Arkadiusz Wesolowski, <a href="/A193257/b193257.txt">Table of n, a(n) for n = 1..200</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/LegendresConstant.html">Legendre's Constant</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeCountingFunction.html">Prime Counting Function</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PrimeNumberTheorem.html">Prime Number Theorem</a>
%F a(n) = floor((10^n)/(log(10^n) - 1)).
%e a(2) = 27 because (10^2)/(log(10^2) - 1) = 27.7379415786....
%t Table[Floor[10^n/(Log[10^n] - 1)], {n, 20}]
%o (Magma) [Floor(10^n/(Log(10^n)-1)) : n in [1..20]]
%o (PARI) for(n=1, 20, print1(floor(10^n/(log(10^n)-1)), ", "))
%o (PARI) a(n)=10^n\(n*log(10)-1) \\ _Charles R Greathouse IV_, Jul 30 2011
%Y Another version of A226744.
%Y Cf. A058289, A006880, A057834, A000720.
%K nonn
%O 1,1
%A _Arkadiusz Wesolowski_, Jul 19 2011
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