A094661 Numerator of the sum of the ratios of consecutive primes.

3, 19, 137, 1289, 16909, 259087, 4975049, 106267661, 2725447213, 85953848147, 2903947942067, 115669053951809, 5061522951820999, 231945249314081827, 11594813068340357459, 650803589794759938517, 40385350464999429101033

Offset: 2

Author

Cino Hilliard, Jun 06 2004

Keywords

• nonn
• frac

Crossrefs

Cf. A000040.

Programs

Mathematica

s=0;lst={};Do[p=Prime[n];r=Prime[n+1];AppendTo[lst,Numerator[s+=r/p]],{n,3*4!}];lst (* Vladimir Joseph Stephan Orlovsky, Oct 24 2009 *)

PARI

consec(n) = { y=0; forprime(x=2,n, y+=nextprime(x+1)/x; z=numerator(y); print1(z",") ) }

Formula

a(n) = numerator(Sum_{k=1..n} prime(k+1)/prime(k)).