A322258 Decimal expansion of exp(-phi/sqrt(5)), where phi is the golden ratio.

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

Offset

0,1

References

J. Sandor and B. Crstici, Handbook of Number Theory II, Springer, 2004, pp. 54-55, p. 182.

Links

Table of n, a(n) for n=0..86.

Don Redmond, Infinite products and Fibonacci numbers, Fib. Quart., Vol. 32, No. 3 (1994), pp. 234-239.

Index entries for transcendental numbers

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]]

Prog

(PARI) exp(-(1+1/sqrt(5))/2) \\ Charles R Greathouse IV, Nov 21 2024

Crossrefs

Cf. A000010, A000032, A000045, A001622, A242671, A322259.

Sequence in context: A245780 A165267 A092159 * A141402 A276619 A145900

Adjacent sequences: A322255 A322256 A322257 * A322259 A322260 A322261

Keyword

nonn,cons,changed

Author

Amiram Eldar, Dec 01 2018

Status

approved