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A265305 Decimal expansion of Sum_{k>=1} (c(2k)-c(2k-1)), where c = convergents to sqrt(8).

%I A265305 #8 Dec 18 2015 11:36:37
%S A265305 1,0,3,4,3,4,8,4,4,0,4,4,1,3,4,3,7,7,2,4,3,9,9,2,8,7,0,4,6,7,7,3,3,8,
%T A265305 4,7,2,2,1,1,0,4,2,7,1,4,6,9,9,9,4,2,1,0,7,0,9,4,3,8,3,3,2,7,4,7,4,3,
%U A265305 7,9,7,1,7,6,4,6,6,0,6,1,7,0,5,9,3,1
%N A265305 Decimal expansion of Sum_{k>=1} (c(2k)-c(2k-1)), where c = convergents to sqrt(8).
%e A265305 sum = 1.0343484404413437724399287046773384722110427146999...
%t A265305 x = Sqrt[8]; z = 600; c = Convergents[x, z];
%t A265305 s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
%t A265305 s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
%t A265305 N[s1 + s2, 200]
%t A265305 RealDigits[s1, 10, 120][[1]]  (* A265303 *)
%t A265305 RealDigits[s2, 10, 120][[1]]  (* A265304 *)
%t A265305 RealDigits[s1 + s2, 10, 120][[1]](* A265305 *)
%Y A265305 Cf. A010466, A265303, A265304, A265288 (guide).
%K A265305 nonn,cons
%O A265305 1,3
%A A265305 _Clark Kimberling_, Dec 13 2015