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A265297 Decimal expansion of sum{x - c(2n-1), n=1,2,...}, where c = convergents to (x = sqrt(5)).

%I A265297 #6 Dec 13 2015 08:05:44
%S A265297 2,3,6,8,4,4,2,4,8,5,7,0,1,4,8,1,8,7,5,9,5,3,8,0,1,7,8,2,2,9,9,0,1,1,
%T A265297 9,4,7,6,0,9,8,0,4,2,0,1,8,2,7,4,6,3,5,3,4,6,5,2,3,3,3,3,0,8,9,6,9,1,
%U A265297 8,8,7,4,4,3,0,3,6,3,8,2,0,4,5,1,0,6
%N A265297 Decimal expansion of sum{x - c(2n-1), n=1,2,...}, where c = convergents to (x = sqrt(5)).
%e A265297 sum = 0.236844248570148187595380178229901194760980420...
%t A265297 x = Sqrt[5]; z = 600; c = Convergents[x, z];
%t A265297 s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
%t A265297 s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
%t A265297 N[s1 + s2, 200]
%t A265297 RealDigits[s1, 10, 120][[1]]  (* A265297 *)
%t A265297 RealDigits[s2, 10, 120][[1]]  (* A265298 *)
%t A265297 RealDigits[s1 + s2, 10, 120][[1]](* A265299 *)
%Y A265297 Cf. A002163, A265298, A265299, A265288 (guide).
%K A265297 nonn,cons
%O A265297 0,1
%A A265297 _Clark Kimberling_, Dec 07 2015