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 A190303 Decimal expansion of sum of alternating series of reciprocals of Ramanujan primes, Sum_{n>=1} (1/R_n)(-1)^(n-1), where R_n is the n-th Ramanujan prime, A104272(n). 0
 4, 4, 6, 6, 8, 4, 3, 0, 7 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Computed 0.446684 for n = 1 to 65536, using Open Office Calc. Next digit expected to be between 2 and 3. By computing all Ramanujan primes less than 10^9, we find that about 9 decimal places of the sum should be correct: 0.446684307 (truncated, not rounded). The following table shows the number of Ramanujan primes between powers of 10 and the sum of the alternating reciprocals of those primes. 1          1      0.50000000000000000 2          9     -0.05765566386047510 3         62      0.00388002010130731 4        487      0.00050881775862179 5       3900     -0.00004384563815649 6      32501     -0.00000552572415587 7     279106      0.00000045427780897 8    2444255      0.00000005495474474 9   21731345     -0.00000000549864067 Total:            0.44668430669928564 - T. D. Noe, May 08 2011 Let E_n denote the error after the first n terms in the series. Then by the Alternating Series Test, 1/R_{n+1} - 1/R_{n+2} < E_n < 1/R_{n+1}. [Jonathan Sondow, May 10 2011] LINKS J. Sondow, Ramanujan primes and Bertrand's postulate, arXiv:0907.5232 [math.NT], 2009-2010. J. Sondow, Ramanujan primes and Bertrand's postulate, Amer. Math. Monthly 116 (2009), 630-635. J. Sondow, J. W. Nicholson, and T. D. Noe, Ramanujan Primes: Bounds, Runs, Twins, and Gaps, J. Integer Seq. 14 (2011) Article 11.6.2 Eric W. Weisstein, Prime Sums FORMULA Sum_{n>=1} (-1)^(n-1)(1/R_n), where R_n is the n-th Ramanujan prime, A104272(n). EXAMPLE 0.446684307... CROSSREFS Cf. A104272, A085548, A078437, A190124. Sequence in context: A111657 A049751 A196594 * A175123 A276679 A163638 Adjacent sequences:  A190300 A190301 A190302 * A190304 A190305 A190306 KEYWORD nonn,cons,more AUTHOR John W. Nicholson, May 07 2011 EXTENSIONS Definition corrected by Jonathan Sondow, May 10 2011 STATUS approved

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Last modified February 27 15:59 EST 2020. Contains 332307 sequences. (Running on oeis4.)