A062742 - OEIS

%I #24 Oct 07 2022 23:59:54

%S 2,1,12,31,69,181,443,1052,2701,6455,15928,40073,100362,251707,637235,

%T 1617175,4124437,10553415,27066974,69709680,179992909,465769803,

%U 1208198526,3140421716,8179002096,21338685407,55762149030,145935689361

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

%H Giovanni Resta, <a href="/A062742/b062742.txt">Table of n, a(n) for n = 1..50</a>

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

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

%F a(n) = A038606(n) = A038624(n) for n >= 3. - _Jaroslav Krizek_, Dec 13 2009

%e 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}

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

%Y Essentially the same as A038624.

%Y Cf. A038606. - _R. J. Mathar_, Jan 30 2009

%K nonn

%O 1,1

%A _Labos Elemer_, Jul 12 2001

%E More terms from _Jason Earls_, May 15 2002

%E a(17)-a(28) from _Farideh Firoozbakht_ and _Robert G. Wilson v_, Sep 13 2005

%E a(29)-a(50) obtained from the values of A038625 computed by _Jan Büthe_. - _Giovanni Resta_, Sep 01 2018