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%I #8 Dec 18 2015 11:35:57
%S 5,0,5,6,1,2,8,8,7,8,9,3,5,2,0,0,1,1,6,8,6,0,7,5,7,4,9,4,2,5,9,5,3,1,
%T 1,9,2,8,1,2,4,5,4,1,8,1,3,3,7,4,3,2,5,9,2,9,1,3,5,6,8,2,0,4,6,7,1,6,
%U 5,0,2,4,3,7,1,3,5,2,0,3,7,2,2,6,2,9
%N Decimal expansion of Sum_{k>=1} (c(2k)-c(2k-1)), where c = convergents to sqrt(6).
%e sum = 0.50561288789352001168607574942595311928124541813374...
%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, A265300, A265301, A265288 (guide).
%K nonn,cons
%O 0,1
%A _Clark Kimberling_, Dec 13 2015
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