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A050499 Nearest integer to n/log(n). 11

%I

%S 3,3,3,3,3,4,4,4,4,5,5,5,5,6,6,6,6,6,7,7,7,7,8,8,8,8,8,9,9,9,9,9,10,

%T 10,10,10,10,11,11,11,11,11,12,12,12,12,12,13,13,13,13,13,14,14,14,14,

%U 14,14,15,15,15,15,15,16,16,16,16,16,16,17,17,17,17

%N Nearest integer to n/log(n).

%C The prime number theorem states that the number of primes <= x is asymptotic to x/log(x).

%C n/log(n)=n/log_10(n) * 1/log(10)=n*log_10(e)/log_10(n)=n*A002285/log_10(n) [From _Eric Desbiaux_, Jun 27 2009]

%C Similar to floor(1/(1-x)) where x^n=1/n. - _Jon Perry_, Oct 29 2013

%D Cf. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Theorem 6.

%H T. D. Noe, <a href="/A050499/b050499.txt">Table of n, a(n) for n=2..10000</a>

%t Table[Round[n/Log[n]],{n,2,80}] (* _Harvey P. Dale_, Nov 03 2013 *)

%o (JavaScript)

%o for (i=1;i<100;i++) {

%o x=Math.pow(1/i,1/i);

%o document.write(Math.floor(1/(1-x))+", ");

%o }

%Y Cf. A000720, A050500, A050501.

%K nonn

%O 2,1

%A _N. J. A. Sloane_, Dec 27 1999

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Last modified October 18 12:18 EDT 2019. Contains 328160 sequences. (Running on oeis4.)