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A083523
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Smallest Fibonacci number divisible by 2^n.
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2
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1, 2, 8, 8, 144, 46368, 4807526976, 51680708854858323072, 5972304273877744135569338397692020533504, 79757008057644623350300078764807923712509139103039448418553259155159833079730688
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OFFSET
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0,2
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COMMENTS
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The index of the Fibonacci numbers above begin: 1, 3, 6, 6 and then doubles thereafter.
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LINKS
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FORMULA
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Sum_{n>=0} 1/a(n) = 19/8 - 1/phi, where phi is the golden ratio (A001622). (End)
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MATHEMATICA
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Do[k = 1; While[ !IntegerQ[ Fibonacci[k]/2^n], k++ ]; Print[ Fibonacci[k]], {n, 0, 10}]
With[{fibs=Fibonacci[Range[1000]]}, Table[SelectFirst[fibs, Divisible[#, 2^n]&], {n, 0, 10}]] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Feb 02 2021 *)
Join[{1, 2, 8}, Table[Fibonacci[3*2^(n - 2)], {n, 3, 9}]] (* Amiram Eldar, Jan 29 2022 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Amarnath Murthy and Meenakshi Srikanth (menakan_s(AT)yahoo.com), May 05 2003
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EXTENSIONS
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STATUS
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approved
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