A053621 Nearest integer to n/(log(n)-1).

-1, -7, 30, 10, 8, 8, 7, 7, 8, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 19, 20, 20, 20, 20, 20, 21, 21, 21, 21, 22, 22, 22

Offset: 1

Author

Henry Bottomley, Mar 21 2000

Keywords

• sign

Comments

n/(log(n)-1) is a better approximation than n/log(n) to pi(n) the number of primes <= n, though worse than the logarithmic integral or the Riemann prime number formula.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• C. K. Caldwell, How Many Primes Are There?
• Pierre Dusart, Estimates of Some Functions Over Primes without R.H., arXiv:1002.0442 [math.NT], 2010.

Crossrefs

Cf. A000720, A047784, A050499, A053620.

Programs

Haskell

a053621 = round . (\x -> x / (log x - 1)) . fromIntegral
-- Reinhard Zumkeller, Apr 30 2014

Magma

[Round(n/(Log(n)-1)): n in [1..80]]; // G. C. Greubel, May 17 2019

Mathematica

Table[Round[n/(Log[n]-1)], {n,1,80}] (* G. C. Greubel, May 17 2019 *)

PARI

vector(80, n, round(n/(log(n)-1))) \\ G. C. Greubel, May 17 2019

Sage

[round(n/(log(n)-1)) for n in (1..80)] # G. C. Greubel, May 17 2019