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A373163
a(n) = numerator of Sum_{k>=0} cos(2k*Pi/3)/n^k.
3
5, 21, 6, 55, 39, 35, 68, 171, 35, 253, 150, 117, 203, 465, 88, 595, 333, 247, 410, 903, 165, 1081, 588, 425, 689, 1485, 266, 1711, 915, 651, 1040, 2211, 391, 2485, 1314, 925, 1463, 3081, 540, 3403, 1785, 1247, 1958, 4095, 713, 4465, 2328, 1617, 2525, 5253
OFFSET
2,1
COMMENTS
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.
Conjecture: the sequence of fractions is completely monotonic.
MATHEMATICA
t = Table[Sum[Cos[2 k Pi/3]/n^k, {k, 0, Infinity}], {n, 2, 60}]
Denominator[t]
Numerator[t]
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Clark Kimberling, Jul 22 2024
STATUS
approved