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  • John W. Nicholson
    Dec 12 8:55 PM
      Here is a gp program (RL[x] is a list of x Ramanujan primes) that I am currently running (I expect it to finish by morning):

      n=1; j=1; c=0.0; limit=10^7;
      while(n<limit,
          if(prime(n)<RL[j],
              {c=c+1/prime(n); n++},
              {c=c-1/RL[j]; n++; j++}
      )
      );
      print(c); 

      Will c converge if limit is set to infinity?

      I realize that this is equivalent to sum(1/p_n) - 2*sum(1/R_j) with both n and j going to infinity, because of not adding 1/p_n when subtracting at p_n=R_j, however there are a slight bit more non-Ramamujan primes to Ramanujan primes. If it does not converge why? If it does to what value?
       
      John W. Nicholson