A050499 Nearest integer to n/log(n).

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.

Links

T. D. Noe, Table of n, a(n) for n=2..10000

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

Cf. A000720, A050500, A050501.

Sequence in context: A332875 A176873 A227727 * A304431 A147752 A236682

Adjacent sequences: A050496 A050497 A050498 * A050500 A050501 A050502

Keyword

nonn

Author

N. J. A. Sloane, Dec 27 1999

Status

approved