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A265298 Decimal expansion of sum{c(2n) - x, n=1,2,...}, where c = convergents to (x = sqrt(5)).

%I A265298 #6 Dec 13 2015 08:05:52
%S A265298 0,1,3,9,7,5,2,9,0,4,8,4,1,6,0,6,9,4,6,3,0,4,3,1,9,3,7,0,2,8,4,6,9,2,
%T A265298 8,1,3,5,3,8,0,0,2,5,5,6,4,1,8,4,2,4,2,7,3,4,1,7,9,8,4,7,0,7,1,5,1,8,
%U A265298 7,0,8,2,4,8,3,8,8,2,4,0,8,6,3,3,5,8
%N A265298 Decimal expansion of sum{c(2n) - x, n=1,2,...}, where c = convergents to (x = sqrt(5)).
%e A265298 sum = 0.01397529048416069463043193702846928135380025564...
%t A265298 x = Sqrt[5]; z = 600; c = Convergents[x, z];
%t A265298 s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
%t A265298 s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
%t A265298 N[s1 + s2, 200]
%t A265298 RealDigits[s1, 10, 120][[1]]  (* A265297 *)
%t A265298 RealDigits[s2, 10, 120][[1]]  (* A265298 *)
%t A265298 RealDigits[s1 + s2, 10, 120][[1]](* A265299 *)
%Y A265298 Cf. A002163, A265297, A265299, A265288 (guide).
%K A265298 nonn,cons
%O A265298 0,3
%A A265298 _Clark Kimberling_, Dec 07 2015