A373017 Decimal expansion of Sum_{k>=0} (sin(k*Pi/5))^2/2^k.

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

Offset: 0

Author

Clark Kimberling, Jul 16 2024

Keywords

• nonn
• cons

Comments

Minimal polynomial is 124x^2 - 150x + 45. - Charles R Greathouse IV, Jul 16 2024

Examples

			0.5507402908669405718610683789823078330135334267835...
		

Links

• Index entries for algebraic numbers, degree 2

Crossrefs

Cf. A373021.

Programs

Mathematica

s = Sum[(Sin[k  Pi/5])^2/2^k, {k, 0, Infinity}]
d = N[s, 100]
First[RealDigits[d]]

PARI

suminf(k=0,(sin(k*Pi/5))^2>>k) \\ Charles R Greathouse IV, Jul 16 2024

PARI

(75-sqrt(45))/124 \\ Charles R Greathouse IV, Jul 16 2024

Formula

Equals (3/124) (25 - sqrt(5)).