%I #12 Dec 28 2023 19:21:38
%S 3,19,137,1289,16909,259087,4975049,106267661,2725447213,85953848147,
%T 2903947942067,115669053951809,5061522951820999,231945249314081827,
%U 11594813068340357459,650803589794759938517,40385350464999429101033
%N Numerator of the sum of the ratios of consecutive primes.
%F a(n) = numerator(Sum_{k=1..n} prime(k+1)/prime(k)).
%t 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 *)
%o (PARI) consec(n) = { y=0; forprime(x=2,n, y+=nextprime(x+1)/x; z=numerator(y); print1(z",") ) }
%Y Cf. A000040.
%K nonn,frac
%O 2,1
%A _Cino Hilliard_, Jun 06 2004