A062742 Index j of prime p(j) such that floor(p(j)/j) = n is first satisfied.

2, 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

Labos Elemer, Jul 12 2001

Keywords

• nonn

Examples

			The q(j)=p(j)/j quotient when the value 14 first appears: {j=251706, p(j)=3523841, q(j)=13.9998291} {251707, 3523901, 14.0000119} {251708, 3523903, 13.9999642} {251709, 3523921, 13.9999801} {251710, 3523957, 14.0000675} {251711, 3523963, 14.0000357}
		

Links

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

Crossrefs

Essentially the same as A038624.

Cf. A038606. - R. J. Mathar, Jan 30 2009

Programs

PARI

{a062742(m)=local(n,j); for(n=1,m,j=1; while(floor(prime(j)/j)!=n,j++); print1(j,","))} a062742(10^7)

Formula

a(n) = Min_{j| floor(p(j)/j) = n}. Note that neither p(j)/j nor floor(p(j)/j) is monotonic.

a(n) = pi(A062743(n)).

a(n) = A038606(n) = A038624(n) for n >= 3. - Jaroslav Krizek, Dec 13 2009

Extensions

More terms from Jason Earls, May 15 2002

a(17)-a(28) from Farideh Firoozbakht and Robert G. Wilson v, Sep 13 2005

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