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A322258 Decimal expansion of exp(-phi/sqrt(5)), where phi is the golden ratio. 1
4, 8, 4, 9, 9, 9, 8, 0, 1, 2, 9, 2, 9, 5, 8, 0, 2, 5, 2, 3, 1, 7, 5, 1, 3, 2, 2, 3, 0, 0, 9, 5, 2, 4, 8, 3, 4, 8, 0, 6, 5, 9, 9, 6, 5, 6, 4, 1, 5, 5, 9, 5, 7, 1, 2, 5, 2, 7, 1, 8, 0, 2, 9, 1, 0, 2, 9, 1, 9, 2, 1, 2, 8, 4, 6, 5, 8, 8, 5, 6, 9, 3, 5, 0, 1, 5, 0 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET
0,1
REFERENCES
J. Sandor and B. Crstici, Handbook of Number Theory II, Springer, 2004, pp. 54-55, p. 182.
LINKS
Don Redmond, Infinite products and Fibonacci numbers, Fib. Quart., Vol. 32, No. 3 (1994), pp. 234-239.
FORMULA
Equals Product_{k>=1} (L(k)/(sqrt(5)*F(k)))^(phi(k)/k), where L(k) and F(k) are the Lucas and Fibonacci numbers, and phi(k) is the Euler totient function.
Equals exp(-A242671).
EXAMPLE
0.48499980129295802523175132230095248348065996564155...
MATHEMATICA
RealDigits[Exp[-GoldenRatio/Sqrt[5]], 10, 120][[1]]
CROSSREFS
Sequence in context: A245780 A165267 A092159 * A141402 A276619 A145900
KEYWORD
nonn,cons
AUTHOR
Amiram Eldar, Dec 01 2018
STATUS
approved

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Last modified May 21 17:21 EDT 2024. Contains 372738 sequences. (Running on oeis4.)