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 A259931 Decimal expansion of the sum of the reciprocals of the averages of adjacent pairs of perfect numbers (A000396). 0
 0, 6, 2, 8, 7, 2, 2, 9, 4, 0, 9, 4, 1, 9, 7, 0, 1, 4, 8, 9, 9, 7, 6, 9, 1, 8, 9, 3, 0, 8, 7, 5, 0, 6, 2, 6, 6, 1, 6, 0, 3, 2, 7, 8, 9, 3, 1, 9, 9, 4, 8, 0, 4, 3, 8, 2, 1, 3, 1, 0, 5, 0, 8, 6, 5, 9, 6, 8, 8, 8, 4, 7, 1, 2, 3, 5, 8, 5, 7, 2, 1, 4, 9, 7, 5, 5, 2, 9, 5, 0, 0, 7, 7, 1, 0, 4, 3, 0, 7, 7, 8, 4, 1, 2, 0, 0 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS Jonathan Bayless and Dominic Klyve, Reciprocal sums as a knowledge metric, Amer Math Monthly 120 (November, 2013) 822-831. Steven Finch, Amicable Pairs and Aliquot Sequences, Oct 31 2013. [Cached copy, with permission of the author] MathOverflow, Sum of the reciprocal of perfect numbers, Jun 10 2012. José Camacho Medina's Matematico Fresnillense, La Constante entre Numeros Perfectos (in Spanish). FORMULA Equals Sum_{n>=1} 2/(A000396(n) + A000396(n+1)). Equals Sum_{n>=1} 1/A259849(n). EXAMPLE =0.0628722940941970148997691893087506266160327893199480438213105086596888471... = 1/17 + 1/262 + 1/4312 + 1/16779232 + 1/4311709696 + 1/73014280192 + ... MATHEMATICA exp = {2, 3, 5, 7, 13, 17, 19, 31, 61, 89, 107, 127, 521} (* see A000043 *); pn[k_] := 2^(exp[[k]] - 1)(2^exp[[k]] - 1); RealDigits[Sum[2/(pn[k] + pn[k + 1]), {k, 1, 12}], 10, 111][[1]] (* Robert G. Wilson v, Dec 15 2015 *) CROSSREFS Cf. A000396. Sequence in context: A155687 A021618 A085589 * A021163 A114866 A248270 Adjacent sequences:  A259928 A259929 A259930 * A259932 A259933 A259934 KEYWORD nonn,cons AUTHOR José de Jesús Camacho Medina, Aug 17 2015 EXTENSIONS More terms from Jon E. Schoenfield, Aug 19 2015 More terms from Robert G. Wilson v, Dec 15 2015 STATUS approved

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Last modified October 22 14:53 EDT 2018. Contains 316490 sequences. (Running on oeis4.)