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

1,1

Links

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

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

Example

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}

Prog

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

Crossrefs

Essentially the same as A038624.

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

Sequence in context: A013161 A012926 A013157 * A009821 A009831 A012931

Adjacent sequences: A062739 A062740 A062741 * A062743 A062744 A062745

Keyword

nonn

Author

Labos Elemer, Jul 12 2001

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

Status

approved