A094662 Prime numerators of the sums of the ratios of consecutive primes.

3, 19, 137, 1289, 4975049, 19374829215705183817985416854342477445596764166957007

Offset: 1

Author

Cino Hilliard, Jun 06 2004

Keywords

• frac
• nonn

Comments

Sum of reciprocals = 0.3941031881461705902079511494...

The next term, A094661(53) ~ 1.497*10^100, is too large to include.

It might be preferable to record the index of these primes in A094661: a(n)=A094661(b(n)) with b=(1,2,3,4,7,32,53,55,94,183,189,...). - M. F. Hasler, Mar 06 2009

Examples

			3/2 + 5/3 + 7/5 + 11/7 + 13/11 + 17/13 + 19/17 = 4975049/510510. 4975049 is prime, the fifth entry in the sequence.
		

Programs

Mathematica

Select[Numerator[Accumulate[#[[2]]/#[[1]]&/@Partition[Prime[Range[ 100]], 2,1]]],PrimeQ] (* Harvey P. Dale, Jun 01 2018 *)

PARI

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

PARI

s=0; for( i=1,999, isprime(numerator(s+=prime(i+1)/prime(i))) & print1(numerator(s)",")) \\ M. F. Hasler, Mar 06 2009

Formula

A094662 = A094661 intersect A000040.

Extensions

Corrected and edited by M. F. Hasler, Mar 07 2009