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 A094663 Prime numerators of the sums of the ratios of consecutive primes. 0
 2, 19, 3023, 3469898586979325623, 2502544963063007045084611872632077 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS Sum of reciprocals = 0.5577902661277818841795751911.. LINKS FORMULA If a(n) = Sum(prime(k)/prime(k+1), k=1..n)) is prime. EXAMPLE 2/3 + 3/5 +5/7 + 7/11 = 3023/1155. 3023 is prime, the third entry in the sequence. MATHEMATICA Select[Numerator/@Accumulate[First[#]/Last[#]&/@ Partition[Prime[ Range[50]], 2, 1]], PrimeQ]  (* Harvey P. Dale, Apr 23 2011 *) PROG (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) } CROSSREFS Sequence in context: A013107 A172028 A024229 * A274762 A091688 A306207 Adjacent sequences:  A094660 A094661 A094662 * A094664 A094665 A094666 KEYWORD frac,nonn AUTHOR Cino Hilliard, Jun 06 2004 EXTENSIONS The next term is too large to include. STATUS approved

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Last modified November 29 14:51 EST 2020. Contains 338769 sequences. (Running on oeis4.)