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

0,1

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.

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).

Example

0.40259263632247824757446721584399016437464148244440...

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]]

Prog

(PARI) exp(-(13-5*sqrt(5))/2) \\ Michel Marcus, Dec 02 2018
(Magma) SetDefaultRealField(RealField(100)); Exp(-(13-5*Sqrt(5))/2); // G. C. Greubel, Dec 16 2018
(Sage) numerical_approx(exp(-(9-5*golden_ratio)), digits=100) # G. C. Greubel, Dec 16 2018

Crossrefs

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

Sequence in context: A021717 A016679 A178903 * A057607 A240943 A271823

Adjacent sequences: A322256 A322257 A322258 * A322260 A322261 A322262

Keyword

nonn,cons

Author

Amiram Eldar, Dec 01 2018

Status

approved