A373022 Decimal expansion of Sum_{k>=0} sin(2k*Pi/5)/2^k.

5, 0, 5, 3, 5, 2, 6, 5, 2, 8, 1, 6, 1, 9, 4, 9, 2, 0, 2, 0, 3, 3, 8, 6, 2, 7, 3, 7, 3, 7, 6, 6, 5, 8, 4, 1, 3, 5, 7, 1, 0, 9, 3, 7, 5, 1, 0, 7, 5, 1, 8, 9, 3, 8, 0, 1, 7, 7, 8, 6, 0, 9, 5, 0, 0, 1, 6, 5, 3, 4, 9, 2, 8, 3, 3, 6, 1, 6, 6, 7, 2, 7, 1, 2, 8, 1

Offset

0,1

Links

Table of n, a(n) for n=0..85.

Formula

Equals sqrt((5 + sqrt(5)]/(12 - 2 sqrt(5)).

Equals (-1)*Sum_{k>=0} sin(8 k*Pi/5)/2^k.

Minimal polynomial: 5 - 265 x^2 + 961 x^4.

Example

0.505352652816194920203386273737665...

Mathematica

{b, m, h} = {2, 5, 2}; s = Sum[Sin[ h k Pi/m]/b^k, {k, 0, Infinity}]
d = N[s, 100]
First[RealDigits[d], 100]

Crossrefs

Cf. A373021 (includes guide to related sequences).

Sequence in context: A337084 A199382 A254289 * A140240 A261839 A091672

Adjacent sequences: A373019 A373020 A373021 * A373023 A373024 A373025

Keyword

nonn,cons

Author

Clark Kimberling, Jul 20 2024

Status

approved