A322258 - OEIS

%I #13 Dec 14 2018 11:28:55

%S 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,

%T 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,

%U 9,2,1,2,8,4,6,5,8,8,5,6,9,3,5,0,1,5,0

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

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

%H Don Redmond, <a href="https://www.fq.math.ca/Scanned/32-3/redmond.pdf">Infinite products and Fibonacci numbers</a>, Fib. Quart., Vol. 32, No. 3 (1994), pp. 234-239.

%F 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.

%F Equals exp(-A242671).

%e 0.48499980129295802523175132230095248348065996564155...

%t RealDigits[Exp[-GoldenRatio/Sqrt[5]], 10, 120][[1]]

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

%K nonn,cons

%O 0,1

%A _Amiram Eldar_, Dec 01 2018