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OEIS Sequences A190124 and A190303

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  • John
    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.
    Message 1 of 2 , Dec 9, 2012
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      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.

      John W. Nicholson
    • Maximilian Hasler
      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
      Message 2 of 2 , Dec 10, 2012
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        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.
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