A193257 Floor((10^n)/(log(10^n) - 1)).

7, 27, 169, 1217, 9512, 78030, 661458, 5740303, 50701542, 454011971, 4110416300, 37550193649, 345618860220, 3201414635780, 29816233849000, 279007258230819, 2621647966812031, 24723998785919976, 233922961602470390, 2219671974013732243

Offset: 1

Author

Arkadiusz Wesolowski, Jul 19 2011

Keywords

• nonn

Comments

lim n -> infinity (log(n) - n/pi(n)) = 1, where pi(n) is the prime counting function.

Examples

			a(2) = 27 because (10^2)/(log(10^2) - 1) = 27.7379415786....
		

References

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

Links

• Arkadiusz Wesolowski, Table of n, a(n) for n = 1..200
• Eric Weisstein's World of Mathematics, Legendre's Constant
• Eric Weisstein's World of Mathematics, Prime Counting Function
• Eric Weisstein's World of Mathematics, Prime Number Theorem

Crossrefs

Another version of A226744.

Cf. A058289, A006880, A057834, A000720.

Programs

Magma

[Floor(10^n/(Log(10^n)-1)) : n in [1..20]]

Mathematica

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

PARI

for(n=1, 20, print1(floor(10^n/(log(10^n)-1)), ", "))

PARI

a(n)=10^n\(n*log(10)-1) \\ Charles R Greathouse IV, Jul 30 2011

Formula

a(n) = floor((10^n)/(log(10^n) - 1)).