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%I #15 Jul 29 2017 08:10:12
%S 5,15005,792070839820228500005
%N Denominators in a product expansion for sqrt(5).
%C Apart from the initial term same as A145275.
%C a(3) has 105 digits and a(4) has 523 digits.
%C 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)*....
%F a(n) = Fibonacci(5^(n+1))/Fibonacci(5^n).
%F a(n) = A219010(n)^2 - A219010(n) - 1.
%F 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.
%F a(n) = Lucas(4*5^n) - Lucas(2*5^n) + 1. - _Ehren Metcalfe_, Jul 29 2017
%o (Maxima) A219011(n):=fib(5^(n+1))/fib(5^n)$
%o makelist(A219011(n),n,0,3);
%Y Cf. A145275, A219010, A219013, A219015.
%K nonn,easy,bref
%O 0,1
%A _Peter Bala_, Nov 09 2012
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