A094661 Numerator of the sum of the ratios of consecutive primes.

3, 19, 137, 1289, 16909, 259087, 4975049, 106267661, 2725447213, 85953848147, 2903947942067, 115669053951809, 5061522951820999, 231945249314081827, 11594813068340357459, 650803589794759938517, 40385350464999429101033

Offset

2,1

Links

Table of n, a(n) for n=2..18.

Formula

a(n) = numerator(Sum_{k=1..n} prime(k+1)/prime(k)).

Mathematica

s=0; lst={}; Do[p=Prime[n]; r=Prime[n+1]; AppendTo[lst, Numerator[s+=r/p]], {n, 3*4!}]; lst (* Vladimir Joseph Stephan Orlovsky, Oct 24 2009 *)

Prog

(PARI) consec(n) = { y=0; forprime(x=2, n, y+=nextprime(x+1)/x; z=numerator(y); print1(z", ") ) }

Crossrefs

Cf. A000040.

Sequence in context: A221297 A138513 A321515 * A094662 A321349 A115750

Adjacent sequences: A094658 A094659 A094660 * A094662 A094663 A094664

Keyword

nonn,frac

Author

Cino Hilliard, Jun 06 2004

Status

approved