This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A259931 #87 Jun 01 2017 13:51:44
%S A259931 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,
%T A259931 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,
%U A259931 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
%N A259931 Decimal expansion of the sum of the reciprocals of the averages of adjacent pairs of perfect numbers (A000396).
%H A259931 Jonathan Bayless and Dominic Klyve, <a href="http://www.jstor.org/stable/10.4169/amer.math.monthly.120.09.822">Reciprocal sums as a knowledge metric</a>, Amer Math Monthly 120 (November, 2013) 822-831.
%H A259931 Steven Finch, <a href="/A000396/a000396.pdf">Amicable Pairs and Aliquot Sequences</a>, Oct 31 2013. [Cached copy, with permission of the author]
%H A259931 MathOverflow, <a href="http://mathoverflow.net/questions/99227/sum-of-the-reciprocal-of-perfect-numbers">Sum of the reciprocal of perfect numbers</a>, Jun 10 2012.
%H A259931 José Camacho Medina's Matematico Fresnillense, <a href="http://matematicofresnillense.blogspot.mx/2015/07/constante-entre-numeros-perfectos.html">La Constante entre Numeros Perfectos</a> (in Spanish).
%F A259931 Equals Sum_{n>=1} 2/(A000396(n) + A000396(n+1)).
%F A259931 Equals Sum_{n>=1} 1/A259849(n).
%e A259931 =0.0628722940941970148997691893087506266160327893199480438213105086596888471...
%e A259931 = 1/17 + 1/262 + 1/4312 + 1/16779232 + 1/4311709696 + 1/73014280192 + ...
%t A259931 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 *)
%Y A259931 Cf. A000396.
%K A259931 nonn,cons
%O A259931 0,2
%A A259931 _José de Jesús Camacho Medina_, Aug 17 2015
%E A259931 More terms from _Jon E. Schoenfield_, Aug 19 2015
%E A259931 More terms from _Robert G. Wilson v_, Dec 15 2015