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%I #12 Aug 28 2021 05:52:20
%S 1,9,4,6,3,0,6,0,4,2,7,2,8,3,5,6,5,4,2,6,0,9,2,7,1,1,0,6,8,7,7,9,5,0,
%T 0,6,0,6,0,9,2,7,4,8,7,9,4,7,5,9,9,7,6,1,5,8,2,8,0,2,5,6,8,7,3,7,1,9,
%U 6,4,8,7,5,1,9,7,5,1,8,7,5,7,4,8,5,6
%N Decimal expansion of the limiting ratio of consecutive terms of A289262.
%F Real root of the equation 2 - 2*x + x^2 - 2*x^3 + x^4 - 2*x^5 + x^6 = 0. - _Vaclav Kotesovec_, Aug 28 2021
%e 1.94630604272835654260927110687795006060927487947599...
%t z = 2000; r = 11/7;
%t u = CoefficientList[Series[1/Sum[Floor[(k + 1)*r] (-x)^k, {k, 0, z}], {x, 0, z}], x]; (* A289262 *)
%t v = N[u[[z]]/u[[z - 1]], 200]
%t RealDigits[v, 10][[1]](* A289267 *)
%Y Cf. A078140 (includes guide to related constants), A289262.
%K nonn,cons,easy
%O 1,2
%A _Clark Kimberling_, Jul 14 2017
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