OFFSET
1,1
COMMENTS
lim n -> infinity (log(n) - n/pi(n)) = 1, where pi(n) is the prime counting function.
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
FORMULA
a(n) = floor((10^n)/(log(10^n) - 1)).
EXAMPLE
a(2) = 27 because (10^2)/(log(10^2) - 1) = 27.7379415786....
MATHEMATICA
Table[Floor[10^n/(Log[10^n] - 1)], {n, 20}]
PROG
(Magma) [Floor(10^n/(Log(10^n)-1)) : n in [1..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
CROSSREFS
KEYWORD
nonn
AUTHOR
Arkadiusz Wesolowski, Jul 19 2011
STATUS
approved