A265304 Decimal expansion of Sum_{k>=1} c(2k), where c = convergents to (x = sqrt(8)).

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

Offset: 0

Author

Clark Kimberling, Dec 13 2015

Keywords

• nonn
• cons

Examples

			sum = 0.176627764305151806435705969450793857731839184448725557757777...
		

Crossrefs

Cf. A010466, A265303, A265305, A265288 (guide).

Programs

Mathematica

x = Sqrt[8]; 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]]  (* A265303 *)
RealDigits[s2, 10, 120][[1]]  (* A265304 *)
RealDigits[s1 + s2, 10, 120][[1]](* A265305 *)