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A219011
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Denominators in a product expansion for sqrt(5).
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4
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OFFSET
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0,1
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COMMENTS
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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)*....
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LINKS
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FORMULA
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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.
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PROG
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(Maxima) A219011(n):=fib(5^(n+1))/fib(5^n)$
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CROSSREFS
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KEYWORD
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nonn,easy,bref
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AUTHOR
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STATUS
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approved
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