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A265302
Decimal expansion of Sum_{k>=1} (c(2k)-c(2k-1)), where c = convergents to sqrt(6).
4
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
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
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Dec 13 2015
STATUS
approved