A322259 Decimal expansion of exp(-9 + 5*phi), where phi is the golden ratio.

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

Offset: 0

Author

Amiram Eldar, Dec 01 2018

Keywords

• nonn
• cons

Examples

			0.40259263632247824757446721584399016437464148244440...
		

Links

• Muniru A Asiru, Table of n, a(n) for n = 0..2000
• Don Redmond, Infinite products and Fibonacci numbers, Fib. Quart., Vol. 32, No. 3 (1994), pp. 234-239.
• Index entries for transcendental numbers

Crossrefs

Cf. A000032, A000045, A001622, A008683, A226765, A322258.

Programs

Magma

SetDefaultRealField(RealField(100)); Exp(-(13-5*Sqrt(5))/2); // G. C. Greubel, Dec 16 2018

Maple

evalf[100](exp(-9+5*(1+sqrt(5))/2)); # Muniru A Asiru, Dec 06 2018

Mathematica

RealDigits[Exp[-9+5*GoldenRatio], 10, 120][[1]]

PARI

exp(-(13-5*sqrt(5))/2) \\ Michel Marcus, Dec 02 2018

Sage

numerical_approx(exp(-(9-5*golden_ratio)), digits=100) # G. C. Greubel, Dec 16 2018

Formula

Equals Product_{k>=1} (L(k)/(sqrt(5)*F(k)))^(mu(k)/k), where L(k) and F(k) are the Lucas and Fibonacci numbers, and mu(k) is the Moebius function.

Equals exp(-A226765).