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

2, 19, 3023, 3469898586979325623, 2502544963063007045084611872632077

Offset: 1

Author

Cino Hilliard, Jun 06 2004

Keywords

• nonn

Comments

The next term is too large to include.

Prime terms of A091852.

Sum of reciprocals = 0.5577902661277818841795751911...

Examples

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

Links

• Amiram Eldar, Table of n, a(n) for n = 1..9

Crossrefs

Cf. A091852.

Programs

Mathematica

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

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) }

Extensions

Offset corrected by Amiram Eldar, Jun 26 2024