A259173 Decimal expansion of the positive solution x to Sum_{k>=1} 1/(k^2 + x) = 1.

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, 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, 8, 6, 2, 3, 2, 7, 5, 1, 8, 6, 8, 0, 7, 7, 6, 2, 7, 2

Offset: 1

Author

José María Grau Ribas, Jun 19 2015

Keywords

• nonn
• cons

Examples

			1.2802016832895660106129188375799642131486184249158504289221305
		

Crossrefs

Cf. A013661, A259171.

Programs

Mathematica

g[n_]:=Sum[1/(k^2+n),{k,Infinity}]; x/.FindRoot[g[x]==1,{x,1},AccuracyGoal->2000,WorkingPrecision-> 2340,MaxIterations->1000]//RealDigits//First
FindRoot[Pi*Sqrt[x]*Coth[Pi*Sqrt[x]] == 2*x+1, {x, 1}, WorkingPrecision->120] (* Vaclav Kotesovec, Jun 28 2015 *)