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Round((10^n)/(log(10^n) - 1)).
2

%I #13 May 21 2014 09:17:27

%S 8,28,169,1218,9512,78030,661459,5740304,50701542,454011971,

%T 4110416301,37550193650,345618860221,3201414635781,29816233849001,

%U 279007258230820,2621647966812031,24723998785919976,233922961602470391,2219671974013732243

%N Round((10^n)/(log(10^n) - 1)).

%D A. M. Legendre, Essai sur la Théorie des Nombres, Paris: Duprat, 1808.

%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) = round((10^n)/(log(10^n) - 1)).

%e a(2) = 28 because (10^2)/(log(10^2) - 1) = 27.7379415786....

%t Table[Round[10^n/(Log[10^n] - 1)], {n, 20}]

%o (PARI) for(n=1, 20, print1(round(10^n/(log(10^n)-1)), ", "));

%Y Another version of A193257.

%Y Cf. A058289, A006880, A057834, A000720.

%K nonn

%O 1,1

%A _Arkadiusz Wesolowski_, Aug 31 2013