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A050499
Nearest integer to n/log(n).
13
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, 10, 10, 10, 10, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 14, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17
OFFSET
2,1
COMMENTS
The prime number theorem states that the number of primes <= x is asymptotic to x/log(x).
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]
Similar to floor(1/(1-x)) where x^n=1/n. - Jon Perry, Oct 29 2013
REFERENCES
Cf. G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, Theorem 6.
MATHEMATICA
Table[Round[n/Log[n]], {n, 2, 80}] (* Harvey P. Dale, Nov 03 2013 *)
PROG
(JavaScript)
for (i=1; i<100; i++) {
x=Math.pow(1/i, 1/i);
document.write(Math.floor(1/(1-x))+", ");
}
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 27 1999
STATUS
approved