A373162 a(n) = denominator of Sum_{k>=0} cos(2k*Pi/3)/n^k.

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.

Links

Table of n, a(n) for n=2..51.

Mathematica

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

Crossrefs

Cf. A373160, A373161, A373163.

Sequence in context: A012490 A354478 A157702 * A063453 A284054 A284786

Adjacent sequences: A373159 A373160 A373161 * A373163 A373164 A373165

Keyword

nonn,frac

Author

Clark Kimberling, Jul 22 2024

Status

approved