A265298 - OEIS

%I #6 Dec 13 2015 08:05:52

%S 0,1,3,9,7,5,2,9,0,4,8,4,1,6,0,6,9,4,6,3,0,4,3,1,9,3,7,0,2,8,4,6,9,2,

%T 8,1,3,5,3,8,0,0,2,5,5,6,4,1,8,4,2,4,2,7,3,4,1,7,9,8,4,7,0,7,1,5,1,8,

%U 7,0,8,2,4,8,3,8,8,2,4,0,8,6,3,3,5,8

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

%e sum = 0.01397529048416069463043193702846928135380025564...

%t x = Sqrt[5]; 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]]  (* A265297 *)

%t RealDigits[s2, 10, 120][[1]]  (* A265298 *)

%t RealDigits[s1 + s2, 10, 120][[1]](* A265299 *)

%Y Cf. A002163, A265297, A265299, A265288 (guide).

%K nonn,cons

%O 0,3

%A _Clark Kimberling_, Dec 07 2015