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%I #12 Jun 01 2018 12:12:09
%S 3,19,137,1289,4975049,
%T 19374829215705183817985416854342477445596764166957007
%N Prime numerators of the sums of the ratios of consecutive primes.
%C Sum of reciprocals = 0.3941031881461705902079511494...
%C The next term, A094661(53) ~ 1.497*10^100, is too large to include.
%C It might be preferable to record the index of these primes in A094661: a(n)=A094661(b(n)) with b=(1,2,3,4,7,32,53,55,94,183,189,...). - _M. F. Hasler_, Mar 06 2009
%F A094662 = A094661 intersect A000040.
%e 3/2 + 5/3 + 7/5 + 11/7 + 13/11 + 17/13 + 19/17 = 4975049/510510. 4975049 is prime, the fifth entry in the sequence.
%t Select[Numerator[Accumulate[#[[2]]/#[[1]]&/@Partition[Prime[Range[ 100]], 2,1]]],PrimeQ] (* _Harvey P. Dale_, Jun 01 2018 *)
%o (PARI) consecpr(n) = { s=0; y=0; forprime(x=2,n, y+=nextprime(x+1)/x; z=numerator(y); s+=1./z; if(isprime(z),print1(z",")) ); print(); print(s) }
%o (PARI) s=0; for( i=1,999, isprime(numerator(s+=prime(i+1)/prime(i))) & print1(numerator(s)",")) \\ _M. F. Hasler_, Mar 06 2009
%K frac,nonn
%O 1,1
%A _Cino Hilliard_, Jun 06 2004
%E Corrected and edited by _M. F. Hasler_, Mar 07 2009