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%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