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%I #7 Nov 21 2013 12:48:19
%S 2,19,3023,3469898586979325623,2502544963063007045084611872632077
%N Prime numerators of the sums of the ratios of consecutive primes.
%C Sum of reciprocals = 0.5577902661277818841795751911..
%F If a(n) = Sum(prime(k)/prime(k+1), k=1..n)) is prime.
%e 2/3 + 3/5 +5/7 + 7/11 = 3023/1155. 3023 is prime, the third entry in the sequence.
%t Select[Numerator/@Accumulate[First[#]/Last[#]&/@ Partition[Prime[ Range[50]],2,1]],PrimeQ] (* _Harvey P. Dale_, Apr 23 2011 *)
%o (PARI) consecpr2(n) = { s=0; y=0; forprime(x=2,n, y+=x/nextprime(x+1); z=numerator(y); s+=1./z; if(isprime(z),print1(z",")) ); print(); print(s) }
%K frac,nonn
%O 2,1
%A _Cino Hilliard_, Jun 06 2004
%E The next term is too large to include.
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