OFFSET
1,2
COMMENTS
By rewriting the sequence of sums as 1 - Product_{n>=1} (1 - 1/prime(n)), one can show that the product goes to zero and the sequence of sums converges to 1. This is interesting because the terms approach 1/(2*prime(n)) for large n, and a sum of such terms might be expected to diverge, since Sum_{n>=1} 1/(2*prime(n)) diverges.
Denominators appear to be given by A060753(n+1). - Peter Kagey, Jun 08 2019
A254196 appears to be a duplicate of this sequence. - Michel Marcus, Aug 05 2019
LINKS
Peter Kagey, Table of n, a(n) for n = 1..400
FORMULA
MATHEMATICA
Table [1- Product[1 - (1/Prime[k])), {i, 1, j}, {j, 1, 20}]; (* This is a table of the individual sums: Sum[Product[ 1 - (1/Prime[k]), {k, n-1}]/Prime[n], {n, 1, 3}], which is the sum of terms of the Mathematica table given in A038111 (three terms, in this example). *)
PROG
(PARI) r(n) = prod(k=1, n-1, (1 - 1/prime(k)))/prime(n);
a(n) = numerator(sum(k=1, n, r(k))); \\ Michel Marcus, Jun 08 2019
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Daniel Tisdale, Jun 12 2009
STATUS
approved