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%I #9 Dec 18 2015 11:23:09
%S 4,5,4,5,8,7,1,1,3,0,6,5,0,7,2,4,7,4,9,9,8,9,7,8,3,3,0,8,0,9,5,4,3,0,
%T 1,3,3,2,5,0,8,5,3,9,7,8,3,5,3,3,9,5,4,2,6,8,1,3,8,8,7,2,6,3,3,6,6,4,
%U 0,3,9,0,4,6,5,0,4,3,5,4,0,9,4,4,5,5
%N Decimal expansion of Sum_{k>=1} (x-c(2k-1)), where c = convergents to (x = sqrt(6)).
%e sum = 0.454587113065072474998978330809543013325085397...
%t x = Sqrt[6]; z = 600; c = Convergents[x, z];
%t s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
%t s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
%t N[s1 + s2, 200]
%t RealDigits[s1, 10, 120][[1]] (* A265300 *)
%t RealDigits[s2, 10, 120][[1]] (* A265301 *)
%t RealDigits[s1 + s2, 10, 120][[1]](* A265302 *)
%Y Cf. A010464, A265301, A265302, A265288 (guide).
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Dec 13 2015
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