I don't understand what does PARI's sumalt() in that case,

when I set the precision to 99, it gives for the alternating sum of

reciprocal Ramanujan primes (

http://oeis.org/A104272)
gp > sumalt(k=1,(-1)^k/R(k))

%223 = -0.446665312087833970450649975341370880057448620155119426658812070...

using only 110 terms.

When I add the first 9000 terms explicitly and use sumalt(.) for k>9000,

then I get

gp > sumalt(k=1,(-1)^k/R(k+9000))+sum(k=1,9000,(-1)^k/R(k))

%235 = -0.44668430894574326535677643569806510481858234696698728898381...

where again sumalt(.) only uses terms 9000..9143.

The result is worse using flag=1 in

"sumalt(X=a,expr,{flag=0}): Cohen-Villegas-Zagier's acceleration of

alternating series expr, X starting at a. flag is optional, and can be

0: default, or 1: uses a slightly different method using Zagier's

polynomials."

Maximilian

R(k)={global(k_max=if(k_max=='k_max,k,max(k_max,k)));k<#r & return(r[k]);r[#r]}

r=A104272

On Sun, Dec 9, 2012 at 9:48 PM, John <reddwarf2956@...> wrote:

>

>

>

> I figure this group might like this.

>

> In the OEIS, the sequences A190124 and A190303 are defined and computed to 0.265563275... and 0.446684307... respectfully.

>

> The ISC and others do not have them.