|
| |
|
|
A219011
|
|
Denominators in a product expansion for sqrt(5).
|
|
4
|
| |
|
|
|
OFFSET
|
0,1
|
|
|
COMMENTS
|
Apart from the initial term same as A145275.
a(3) has 105 digits and a(4) has 523 digits.
The product expansion in question is sqrt(5) = product {n = 0..inf} (1 + 2*A219010(n)/A219011(n)) = (1 + 6/5)*(1 + 246/15005)*(1 + 56287506246/792070839820228500005)*....
|
|
|
LINKS
|
|
|
|
FORMULA
|
a(n) = Fibonacci(5^(n+1))/Fibonacci(5^n).
Recurrence equation: a(n+1) = 5/2*(a(n)^4 - a(n)^2)*sqrt(4*a(n) + 5) + a(n)^5 + 15/2*a(n)^4 - 25/2*a(n)^2 + 5 with initial condition a(0) = 5.
|
|
|
PROG
|
(Maxima) A219011(n):=fib(5^(n+1))/fib(5^n)$
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
nonn,easy,bref
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
