A265303 Decimal expansion of Sum_{k>=1} (x-c(2k-1)), where c = convergents to (x = sqrt(8)).

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

Offset: 0

Author

Clark Kimberling, Dec 13 2015

Keywords

• nonn
• cons

Examples

			sum = 0.8577206761361919660042227352265446144...
		

Crossrefs

Cf. A010466, A265304, 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 *)