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Prime numerators of the sums of the ratios of consecutive primes.
1

%I #22 Jun 27 2024 01:40:49

%S 2,19,3023,3469898586979325623,2502544963063007045084611872632077

%N Prime numerators of the sums of the ratios of consecutive primes.

%C The next term is too large to include.

%C Prime terms of A091852.

%C Sum of reciprocals = 0.5577902661277818841795751911...

%H Amiram Eldar, <a href="/A094663/b094663.txt">Table of n, a(n) for n = 1..9</a>

%e 3023 is a term since 2/3 + 3/5 + 5/7 + 7/11 = 3023/1155 and 3023 is prime.

%t Select[Numerator/@Accumulate[First[#]/Last[#]&/@ Partition[Prime[ Range[50]],2,1]],PrimeQ] (* _Harvey P. Dale_, Apr 23 2011 *)

%o (PARI) consecpr2(n) = {my(s=0, y=0, z); forprime(x=2,n, y+=x/nextprime(x+1); z=numerator(y); s+=1./z; if(isprime(z),print1(z", ")) ); print(); print(s) }

%Y Cf. A091852.

%K nonn

%O 1,1

%A _Cino Hilliard_, Jun 06 2004

%E Offset corrected by _Amiram Eldar_, Jun 26 2024