A038624 Values of pi(x) where x exceeds n * pi(x).

1, 1, 12, 31, 69, 181, 443, 1052, 2701, 6455, 15928, 40073, 100362, 251707, 637235, 1617175, 4124437, 10553415, 27066974, 69709680, 179992909, 465769803, 1208198526, 3140421716, 8179002096, 21338685407, 55762149030, 145935689361

Offset: 1

Author

Jud McCranie

Keywords

• nonn

Comments

"Exceeds" can be interpreted as ">" or ">=" since the corresponding primes are never multiples of their indices. - R. J. Mathar, Jun 08 2008

Equivalently, a(n) = minimal k such that prime(k)/k >= n. - Enoch Haga, Oct 19 2007

a(n) = A062742(n) = A038606(n) for n >= 3. - Jaroslav Krizek, Dec 13 2009

Examples

			x exceeds 3*pi(x) when pi(x)=12, so a(3)=12
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..50

Crossrefs

Cf. A038623-A038627.

Essentially the same as A062742.

Cf. A038606 (variant).

Programs

Mathematica

Join[{k = 1}, Table[While[Prime[k]/k < n, k++]; k, {n, 2, 18}]] (* Jayanta Basu, Jul 10 2013 *)

Extensions

a(24)-a(28) from Robert G. Wilson v, Sep 26 2005

Edited by N. J. A. Sloane, Jun 30 2008 at the suggestion of R. J. Mathar.

a(29)-a(50) obtained from the values of A038625 computed by Jan Büthe. - Giovanni Resta, Sep 01 2018