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A219011
Denominators in a product expansion for sqrt(5).
4
5, 15005, 792070839820228500005
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)*....
FORMULA
a(n) = Fibonacci(5^(n+1))/Fibonacci(5^n).
a(n) = A219010(n)^2 - A219010(n) - 1.
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.
a(n) = Lucas(4*5^n) - Lucas(2*5^n) + 1. - Ehren Metcalfe, Jul 29 2017
PROG
(Maxima) A219011(n):=fib(5^(n+1))/fib(5^n)$
makelist(A219011(n), n, 0, 3);
CROSSREFS
KEYWORD
nonn,easy,bref
AUTHOR
Peter Bala, Nov 09 2012
STATUS
approved