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A265299 Decimal expansion of sum{c(2n) - c(2n-1), n=1,2,...}, where c = convergents to (x = sqrt(5)).

%I A265299 #6 Dec 13 2015 08:06:04
%S A265299 2,5,0,8,1,9,5,3,9,0,5,4,3,0,8,8,8,2,2,2,5,8,1,2,1,1,5,2,5,8,3,7,0,4,
%T A265299 7,6,1,1,4,7,8,0,6,7,5,8,2,4,5,8,8,7,8,0,8,0,7,0,3,1,8,0,1,6,1,2,1,0,
%U A265299 5,9,5,6,9,1,4,2,4,6,2,2,9,0,8,4,6,5
%N A265299 Decimal expansion of sum{c(2n) - c(2n-1), n=1,2,...}, where c = convergents to (x = sqrt(5)).
%e A265299 sum = 0.25081953905430888222581211525837047611...
%t A265299 x = Sqrt[5]; z = 600; c = Convergents[x, z];
%t A265299 s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
%t A265299 s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
%t A265299 N[s1 + s2, 200]
%t A265299 RealDigits[s1, 10, 120][[1]]  (* A265297 *)
%t A265299 RealDigits[s2, 10, 120][[1]]  (* A265298 *)
%t A265299 RealDigits[s1 + s2, 10, 120][[1]](* A265299 *)
%Y A265299 Cf. A002163, A265297, A265298, A265288 (guide).
%K A265299 nonn,cons
%O A265299 0,1
%A A265299 _Clark Kimberling_, Dec 07 2015