A062072 Continued fraction expansion of Fibonacci factorial constant.

1, 4, 2, 2, 3, 2, 15, 9, 1, 2, 1, 2, 15, 7, 6, 21, 3, 5, 1, 23, 1, 11, 1, 7, 1, 3, 1, 12, 2, 1, 1, 1, 7, 1, 3, 1, 12, 2, 1, 2, 2, 9, 27, 1, 1, 1, 1, 2, 19, 3, 8, 1, 1, 15, 3, 1, 2, 1, 1, 1, 3, 2, 3, 8, 1, 1, 14, 1, 49, 2, 1, 17, 4, 2, 1, 2, 2, 1, 3, 1, 5, 1, 1, 3, 1, 2, 1, 4, 1, 2, 5, 1, 3, 2, 1, 1, 2, 6

Offset: 0

Author

Jason Earls, Jun 27 2001

Keywords

• easy
• nonn
• cofr

Examples

			1.2267420107203532444176302...
		

References

• R. Graham, D. E. Knuth, O. Patashnik, Concrete Mathematics, Addison Wesley, 1990, pp. 478, 571.

Links

• Harry J. Smith, Table of n, a(n) for n = 0..4999
• Simon Plouffe, Plouffe's Inverter

Crossrefs

Cf. A062073 (decimal expansion).

Programs

PARI

\p 500 a=-1/(1/2+sqrt(5)/2)^2; contfrac(prod(n=1,17000,(1-a^n)))

PARI

{ allocatemem(932245000); default(realprecision, 5300); p=-1/(1/2 + sqrt(5)/2)^2; x=contfrac(prodinf(k=1, 1-p^k)); for (n=1, 5000, write("b062072.txt", n-1, " ", x[n])) } \\ Harry J. Smith, Jul 31 2009

Formula

C = (1-a)*(1-a^2)*(1-a^3)... 1.2267420... where a = -1/phi^2 and where phi is the Golden ratio = 1/2 + sqrt(5)/2.

Extensions

Offset changed by Andrew Howroyd, Aug 04 2024