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

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, 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, 5, 9, 5, 6, 9, 1, 4, 2, 4, 6, 2, 2, 9, 0, 8, 4, 6, 5

Offset: 0

Author

Clark Kimberling, Dec 07 2015

Keywords

• nonn
• cons

Examples

			sum = 0.25081953905430888222581211525837047611...
		

Crossrefs

Cf. A002163, A265297, A265298, A265288 (guide).

Programs

Mathematica

x = Sqrt[5]; z = 600; c = Convergents[x, z];
s1 = Sum[x - c[[2 k - 1]], {k, 1, z/2}]; N[s1, 200]
s2 = Sum[c[[2 k]] - x, {k, 1, z/2}]; N[s2, 200]
N[s1 + s2, 200]
RealDigits[s1, 10, 120][[1]]  (* A265297 *)
RealDigits[s2, 10, 120][[1]]  (* A265298 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265299 *)