A373160 a(n) = denominator of Sum_{k>=0} cos(k*Pi/3)/n^k.

1, 14, 13, 14, 31, 86, 19, 146, 91, 74, 133, 314, 61, 422, 241, 182, 307, 686, 127, 842, 463, 338, 553, 1202, 217, 1406, 757, 542, 871, 1862, 331, 2114, 1123, 794, 1261, 2666, 469, 2966, 1561, 1094, 1723, 3614, 631, 3962, 2071, 1442, 2257, 4706, 817, 5102

Offset

2,2

Comments

The first five fractions are 1/1, 15/14, 14/13, 15/14, 33/31; beginning at 14/13 the sequence of fractions is strictly decreasing with limit 1.

Links

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

Mathematica

t = Table[Sum[Cos[k Pi/3]/n^k, {k, 0, Infinity}], {n, 2, 60}]
Denominator[t]
(* or *)
Denominator[Table[(n*(2*n - 1))/(2*(n^2 - n + 1)), {n, 2, 100}]] (* Vaclav Kotesovec, May 28 2024 *)

Crossrefs

Cf. A373161, A373162, A373163.

Sequence in context: A023456 A261305 A055125 * A206564 A076158 A174160

Adjacent sequences: A373157 A373158 A373159 * A373161 A373162 A373163

Keyword

nonn,frac

Author

Clark Kimberling, May 28 2024

Status

approved