%I #4 Jul 25 2024 14:07:02

%S 7,26,7,62,43,38,73,182,37,266,157,122,211,482,91,614,343,254,421,926,

%T 169,1106,601,434,703,1514,271,1742,931,662,1057,2246,397,2522,1333,

%U 938,1483,3122,547,3446,1807,1262,1981,4142,721,4514,2353,1634,2551,5306

%N a(n) = denominator of Sum_{k>=0} cos(2k*Pi/3)/n^k.

%C The first five fractions are 5/7, 21/26, 6/7, 55/62, 39/43; the sequence of fractions is strictly increasing with limit 1.

%C Conjecture: the sequence of fractions is completely monotonic.

%t t = Table[Sum[Cos[2 k Pi/3]/n^k, {k, 0, Infinity}], {n, 2, 60}]

%t Denominator[t]

%t Numerator[t]

%Y Cf. A373160, A373161, A373163.

%K nonn,frac

%O 2,1

%A _Clark Kimberling_, Jul 22 2024