A094663 Prime numerators of the sums of the ratios of consecutive primes.

2, 19, 3023, 3469898586979325623, 2502544963063007045084611872632077

Offset

2,1

Comments

Sum of reciprocals = 0.5577902661277818841795751911..

Links

Table of n, a(n) for n=2..6.

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: A172028 A365050 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