%I #6 Aug 28 2021 04:51:45
%S 1,8,7,8,3,1,9,9,8,2,6,4,7,6,2,0,1,7,3,5,0,4,7,6,9,5,0,3,8,8,6,7,6,3,
%T 4,2,0,2,8,7,5,0,7,5,9,9,5,0,8,7,2,9,0,0,8,5,9,1,4,7,9,3,0,9,7,7,0,4,
%U 5,9,6,8,1,2,1,1,3,6,5,0,2,3,4,4,9,1
%N Decimal expansion of the limiting ratio of consecutive terms of A289912.
%e 1.87831998264762017350476950388676342028750759950872900...
%t z = 100; r = Sqrt[2];
%t u = CoefficientList[Series[1/Sum[Round[(k + 1)*r] (x)^k, {k, 0, z}], {x, 0, z}],
%t x]; (* A289912 *)
%t v = N[u[[z]]/u[[z  1]], 200]
%t d = RealDigits[v, 10][[1]] (* A289913 *)
%Y Cf. A078140 (includes guide to related constants), A289912.
%K nonn,cons,easy
%O 1,2
%A _Clark Kimberling_, Jul 18 2017
