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A192222
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a(n) = Fibonacci(2^n + 1).
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7
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OFFSET
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0,2
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COMMENTS
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a(n) is the numerator of the n-th iterate when Newton's method is applied to the function x^2 - x - 1 with initial guess x = 1. The n-th iterate is a(n)/A058635(n). - Jason Zimba, Jan 20 2023
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LINKS
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FORMULA
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Product_{n>0} (1 + 1/a(n)) = 3/phi = A134973, where phi = (1+sqrt(5))/2 is the golden mean.
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MATHEMATICA
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Table[Fibonacci[2^n + 1], {n, 0, 10}] (* T. D. Noe, Jan 11 2012 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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