A265302 Decimal expansion of Sum_{k>=1} (c(2k)-c(2k-1)), where c = convergents to sqrt(6).

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

Offset

0,1

Links

Table of n, a(n) for n=0..85.

Example

sum = 0.50561288789352001168607574942595311928124541813374...

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 *)

Crossrefs

Cf. A010464, A265300, A265301, A265288 (guide).

Sequence in context: A156716 A055510 A200397 * A228764 A200631 A201939

Adjacent sequences: A265299 A265300 A265301 * A265303 A265304 A265305

Keyword

nonn,cons

Author

Clark Kimberling, Dec 13 2015

Status

approved