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A111035
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Numbers n that divide the sum of the first n nonzero Fibonacci numbers.
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11
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1, 2, 24, 48, 72, 77, 96, 120, 144, 192, 216, 240, 288, 319, 323, 336, 360, 384, 432, 480, 576, 600, 648, 672, 720, 768, 864, 960, 1008, 1080, 1104, 1152, 1200, 1224, 1296, 1320, 1344, 1368, 1440, 1517, 1536, 1680, 1728, 1800, 1920, 1944, 2016, 2064, 2160
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OFFSET
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1,2
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COMMENTS
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The sum of the first n nonzero Fibonacci numbers is F(n+2)-1, sequence A000071. Knott discusses the factorization of these numbers. Most of the terms are divisible by 24. - T. D. Noe, Oct 10 2005, edited by M. F. Hasler, Mar 01 2020
All terms are either multiples of 24 (cf. A124455) or odd (cf. A331976) or congruent to 2 (mod 12), cf. A331870 where this statement is proved. - M. F. Hasler, Mar 01 2020
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LINKS
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FORMULA
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EXAMPLE
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2 | 4, 24 | 121392, 48 | 12586269024, ... [Corrected by M. F. Hasler, Feb 06 2020]
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MAPLE
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select(n-> irem(combinat[fibonacci](n+2)-1, n)=0, [$1..3000])[]; # G. C. Greubel, Feb 03 2020
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MATHEMATICA
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Select[Range[3000], Mod[Fibonacci[ #+2]-1, # ]==0&] (* T. D. Noe, Oct 06 2005 *)
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PROG
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(Magma) [1] cat [n: n in [1..3000] | Fibonacci(n+2) mod n eq 1 ]; // G. C. Greubel, Feb 03 2020
(Sage) [n for n in (1..3000) if mod(fibonacci(n+2), n)==1 ] # G. C. Greubel, Feb 03 2020
(GAP) Filtered([1..3000], n-> ((Fibonacci(n+2)-1) mod n)=0 ); # G. C. Greubel, Feb 03 2020
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CROSSREFS
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Cf. A111058 (the analog for Lucas numbers).
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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