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A265304 Decimal expansion of Sum_{k>=1} c(2k), where c = convergents to (x = sqrt(8)).

%I A265304 #6 Dec 18 2015 11:36:26
%S A265304 1,7,6,6,2,7,7,6,4,3,0,5,1,5,1,8,0,6,4,3,5,7,0,5,9,6,9,4,5,0,7,9,3,8,
%T A265304 5,7,7,3,1,8,3,9,1,8,4,4,4,8,7,2,5,5,5,7,7,5,7,7,7,7,4,0,7,0,2,8,2,6,
%U A265304 5,8,5,4,9,0,5,2,7,5,4,5,2,9,4,0,8,7
%N A265304 Decimal expansion of Sum_{k>=1} c(2k), where c = convergents to (x = sqrt(8)).
%e A265304 sum = 0.176627764305151806435705969450793857731839184448725557757777...
%t A265304 x = Sqrt[8]; z = 600; c = Convergents[x, z];
%t A265304 s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
%t A265304 s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
%t A265304 N[s1 + s2, 200]
%t A265304 RealDigits[s1, 10, 120][[1]]  (* A265303 *)
%t A265304 RealDigits[s2, 10, 120][[1]]  (* A265304 *)
%t A265304 RealDigits[s1 + s2, 10, 120][[1]](* A265305 *)
%Y A265304 Cf. A010466, A265303, A265305, A265288 (guide).
%K A265304 nonn,cons
%O A265304 0,2
%A A265304 _Clark Kimberling_, Dec 13 2015