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A372048
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The index of the largest Fibonacci number that divides the sum of Fibonacci numbers with indices 1 through n.
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4
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2, 3, 2, 2, 4, 5, 4, 4, 6, 7, 6, 6, 8, 9, 8, 8, 10, 11, 10, 10, 12, 13, 12, 12, 14, 15, 14, 14, 16, 17, 16, 16, 18, 19, 18, 18, 20, 21, 20, 20, 22, 23, 22, 22, 24, 25, 24, 24, 26, 27, 26, 26, 28, 29, 28, 28, 30, 31, 30, 30, 32, 33, 32, 32, 34, 35, 34, 34, 36, 37, 36, 36, 38, 39, 38, 38, 40, 41, 40, 40
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OFFSET
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1,1
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COMMENTS
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The sum of the first n Fibonacci numbers is sequence A000071.
When we divide the sum by the largest Fibonacci number that divides the sum, we always get a Lucas number.
For n > 3, a(n+4) = a(n)+1.
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LINKS
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EXAMPLE
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The sum of the first ten Fibonacci numbers is 143. The largest Fibonacci that divides this sum is 13, the seventh Fibonacci number. Thus, a(10) = 7. After the division we get 143/13 = 11, the fifth Lucas number.
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MATHEMATICA
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LinearRecurrence[{2, -2, 2, -1}, {2, 3, 2, 2}, 80] (* James C. McMahon, Apr 30 2024 *)
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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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