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A265301 Decimal expansion of Sum_{k>=1} c(2k), where c = convergents to (x = sqrt(6)).

%I A265301 #6 Dec 18 2015 11:35:45
%S A265301 5,1,0,2,5,7,7,4,8,2,8,4,4,7,5,3,6,6,8,7,0,9,7,4,1,8,6,1,6,4,1,0,1,0,
%T A265301 5,9,5,6,1,6,0,0,2,0,2,9,8,4,0,3,7,1,6,6,0,9,9,6,8,0,9,4,1,3,0,5,2,4,
%U A265301 6,3,3,9,0,6,3,0,8,4,9,6,2,8,1,7,3,5
%N A265301 Decimal expansion of Sum_{k>=1} c(2k), where c = convergents to (x = sqrt(6)).
%e A265301 sum = 0.0510257748284475366870974186164101059561600202984037166...
%t A265301 x = Sqrt[6]; z = 600; c = Convergents[x, z];
%t A265301 s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
%t A265301 s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
%t A265301 N[s1 + s2, 200]
%t A265301 RealDigits[s1, 10, 120][[1]]  (* A265300 *)
%t A265301 RealDigits[s2, 10, 120][[1]]  (* A265301 *)
%t A265301 RealDigits[s1 + s2, 10, 120][[1]](* A265302 *)
%Y A265301 Cf. A010464, A265300, A265302, A265288 (guide).
%K A265301 nonn,cons
%O A265301 0,1
%A A265301 _Clark Kimberling_, Dec 13 2015