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Smallest x such that Floor[A000040(x)/A002808(x)]=n.
6

%I #9 Mar 16 2015 22:53:25

%S 5,16,40,98,241,591,1393,3386,8313,20393,50189,123972,308917,776173,

%T 1953900,4942615,12556599,32045879,82012870,210587095,542262360,

%U 1400124552,3623612454,9398492120,24425121427,63595807021,165867439024

%N Smallest x such that Floor[A000040(x)/A002808(x)]=n.

%C Smallest k such that prime(k) > n*composite(k).

%e n=39: p(39)=167, c(39)=56, q=2.98; n=40: p(40)=173, c(40)=57, q=3.035, so a(3)=40.

%t f[x_] := Floor[Prime[x] / FixedPoint[x + PrimePi[ # ] + 1 &, x]]; t=Table[0, {30}]; Do[ s = f[n]; If[ s < 31 && t[[s]]==0, t[[s]] = n], {n, 1000000}]; t

%o (PARI) nextcomposite(k)=if(k<3,4,if(isprime(k),k+1,k));

%o (PARI) k=1;p=2;q=4;for(n=1,19, while(p<=n*q,p=nextprime(p+1);q=nextcomposite(q+1);k++);print1(k,","))

%Y Cf. A000040, A002808, A073458.

%K nonn

%O 1,1

%A _Labos Elemer_, Aug 02 2002

%E a(12)-a(19) and PARI code from _Klaus Brockhaus_, Apr 26 2004

%E a(20)-a(27) from _Robert G. Wilson v_, Apr 28 2004