A073459 Smallest x such that Floor[A000040(x)/A002808(x)]=n.

5, 16, 40, 98, 241, 591, 1393, 3386, 8313, 20393, 50189, 123972, 308917, 776173, 1953900, 4942615, 12556599, 32045879, 82012870, 210587095, 542262360, 1400124552, 3623612454, 9398492120, 24425121427, 63595807021, 165867439024

Offset: 1

Author

Labos Elemer, Aug 02 2002

Keywords

• nonn

Comments

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

Examples

			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.
		

Crossrefs

Cf. A000040, A002808, A073458.

Programs

Mathematica

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

PARI

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

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,","))

Extensions

a(12)-a(19) and PARI code from Klaus Brockhaus, Apr 26 2004

a(20)-a(27) from Robert G. Wilson v, Apr 28 2004