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Decimal expansion of the limiting ratio of consecutive terms of A288229.
2

%I #6 Aug 28 2021 04:47:18

%S 1,9,8,7,8,4,4,5,1,7,5,0,0,9,7,0,2,1,3,2,0,8,5,9,5,2,9,7,1,2,2,2,4,8,

%T 2,4,2,8,5,1,4,1,9,5,8,8,4,5,8,3,7,6,7,7,9,8,0,8,2,6,9,4,8,9,4,1,0,4,

%U 6,6,5,5,2,7,1,4,3,7,9,6,1,2,3,8,6,1

%N Decimal expansion of the limiting ratio of consecutive terms of A288229.

%e 1.9878445175009702132085952971222...

%t z = 2000; r = Pi/2;

%t u = CoefficientList[Series[1/Sum[Floor[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}], x]; (* A288229 *)

%t v = N[u[[z]]/u[[z - 1]], 200]

%t RealDigits[v, 10][[1]](* A288239 *)

%Y Cf. A288229, A078140 (includes guide to related constants).

%K nonn,cons,easy

%O 1,2

%A _Clark Kimberling_, Jul 11 2017