%I
%S 1,2,4,14,22,48,52,88,310,796
%N Numbers n such that numerator(sum(i=1,n, prime(i)/prime(i+1))) is prime.
%C No more terms up to and including n=2000.  _Harvey P. Dale_, Dec 16 2018
%e a(2)=2 2/3 + 3/5 = 19/15 and 19 is prime and prime(2+1)=5.
%e a(3)=4 because 2/3+3/5+5/7+7/11 = 3023/1155 and 3023 is prime and prime(4+1)=11.
%t Position[Numerator[Accumulate[#[[1]]/#[[2]]&/@Partition[Prime[ Range[ 800]],2,1]]],_?(PrimeQ[#]&)]//Flatten (* _Harvey P. Dale_, Dec 16 2018 *)
%o (PARI) pp(n)= s=0; for (i=1,n,s=s+prime(i)/prime(i+1));return(s); for (i=1,800,if(isprime(numerator(pp(i))),print(i)))
%K hard,nonn
%O 1,2
%A mohammed bouayoun (bouyao(AT)wanadoo.fr), Feb 16 2004
