A265301 Decimal expansion of Sum_{k>=1} c(2k), where c = convergents to (x = sqrt(6)).

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

Offset: 0

Author

Clark Kimberling, Dec 13 2015

Keywords

• nonn
• cons

Examples

			sum = 0.0510257748284475366870974186164101059561600202984037166...
		

Crossrefs

Cf. A010464, A265300, A265302, A265288 (guide).

Programs

Mathematica

x = Sqrt[6]; 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]]  (* A265300 *)
RealDigits[s2, 10, 120][[1]]  (* A265301 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265302 *)