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A265303 Decimal expansion of Sum_{k>=1} (x-c(2k-1)), where c = convergents to (x = sqrt(8)).

%I A265303 #8 Dec 18 2015 11:36:14
%S A265303 8,5,7,7,2,0,6,7,6,1,3,6,1,9,1,9,6,6,0,0,4,2,2,2,7,3,5,2,2,6,5,4,4,6,
%T A265303 1,4,4,7,9,2,0,3,5,3,0,2,5,1,2,1,6,5,4,9,3,3,6,6,0,5,9,2,0,4,4,6,1,1,
%U A265303 3,8,6,2,7,4,1,3,3,0,7,1,7,6,5,2,2,8
%N A265303 Decimal expansion of Sum_{k>=1} (x-c(2k-1)), where c = convergents to (x = sqrt(8)).
%e A265303 sum = 0.8577206761361919660042227352265446144...
%t A265303 x = Sqrt[8]; z = 600; c = Convergents[x, z];
%t A265303 s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
%t A265303 s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
%t A265303 N[s1 + s2, 200]
%t A265303 RealDigits[s1, 10, 120][[1]]  (* A265303 *)
%t A265303 RealDigits[s2, 10, 120][[1]]  (* A265304 *)
%t A265303 RealDigits[s1 + s2, 10, 120][[1]](* A265305 *)
%Y A265303 Cf. A010466, A265304, A265305, A265288 (guide).
%K A265303 nonn,cons
%O A265303 0,1
%A A265303 _Clark Kimberling_, Dec 13 2015