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A373017
Decimal expansion of Sum_{k>=0} (sin(k*Pi/5))^2/2^k.
1
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
0,1
COMMENTS
Minimal polynomial is 124x^2 - 150x + 45. - Charles R Greathouse IV, Jul 16 2024
FORMULA
Equals (3/124) (25 - sqrt(5)).
EXAMPLE
0.5507402908669405718610683789823078330135334267835...
MATHEMATICA
s = Sum[(Sin[k Pi/5])^2/2^k, {k, 0, Infinity}]
d = N[s, 100]
First[RealDigits[d]]
PROG
(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
CROSSREFS
Cf. A373021.
Sequence in context: A357715 A200257 A236023 * A200516 A233383 A144184
KEYWORD
nonn,cons
AUTHOR
Clark Kimberling, Jul 16 2024
STATUS
approved