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A373162
a(n) = denominator of Sum_{k>=0} cos(2k*Pi/3)/n^k.
3
7, 26, 7, 62, 43, 38, 73, 182, 37, 266, 157, 122, 211, 482, 91, 614, 343, 254, 421, 926, 169, 1106, 601, 434, 703, 1514, 271, 1742, 931, 662, 1057, 2246, 397, 2522, 1333, 938, 1483, 3122, 547, 3446, 1807, 1262, 1981, 4142, 721, 4514, 2353, 1634, 2551, 5306
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