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%I #21 Jul 04 2015 02:43:29
%S 1,2,8,0,2,0,1,6,8,3,2,8,9,5,6,6,0,1,0,6,1,2,9,1,8,8,3,7,5,7,9,9,6,4,
%T 2,1,3,1,4,8,6,1,8,4,2,4,9,1,5,8,5,0,4,2,8,9,2,2,1,3,0,5,7,9,6,1,5,1,
%U 8,6,2,3,2,7,5,1,8,6,8,0,7,7,6,2,7,2
%N Decimal expansion of the positive solution x to Sum_{k>=1} 1/(k^2 + x) = 1.
%e 1.2802016832895660106129188375799642131486184249158504289221305
%t g[n_]:=Sum[1/(k^2+n),{k,Infinity}]; x/.FindRoot[g[x]==1,{x,1},AccuracyGoal->2000,WorkingPrecision-> 2340,MaxIterations->1000]//RealDigits//First
%t FindRoot[Pi*Sqrt[x]*Coth[Pi*Sqrt[x]] == 2*x+1, {x, 1}, WorkingPrecision->120] (* _Vaclav Kotesovec_, Jun 28 2015 *)
%Y Cf. A013661, A259171.
%K nonn,cons
%O 1,2
%A _José María Grau Ribas_, Jun 19 2015