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Search: id:A023172
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| A023172 |
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Numbers n such that n divides Fibonacci(n). |
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+0
15
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| 1, 5, 12, 24, 25, 36, 48, 60, 72, 96, 108, 120, 125, 144, 168, 180, 192, 216, 240, 288, 300, 324, 336, 360, 384, 432, 480, 504, 540, 552, 576, 600, 612, 625, 648, 660, 672, 684, 720, 768, 840, 864, 900, 960, 972, 1008, 1080, 1104, 1152, 1176, 1200, 1224, 1296, 1320
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Sequence contains all powers of 5, infinitely many multiples of 12 and other numbers (including some factors of Fib(5^k), e.g. 75025).
If m is in this sequence then 5*m is (since 5*m divides 5*F(m) which in turn divides F(5*m)). Also, if m is in this sequence then F(m) is in this sequence (since if gcd(F(m),m)=m then gcd(F(F(m)),F(m)) = F(gcd(F(m),m)) = F(m)). [From Max Alekseyev (maxale(AT)gmail.com), Sep 20 2009]
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REFERENCES
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S. Wolfram, "A new kind of science", p. 891
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..500
F. Lengyel, Divisibility Properties by Multisection
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MATHEMATICA
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a=0; b=1; c=1; Do[a=b; b=c; c=a+b; If[Mod[c, n]==0, Print[n]], {n, 3, 1500}]
Select[Range[1350], Mod[Fibonacci[ # ], # ]==0&] (from Harvey Dale)
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CROSSREFS
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Cf. A000350. See A127787 for an essentially identical sequence.
Sequence in context: A000327 A130624 A066869 this_sequence A100479 A018806 A126880
Adjacent sequences: A023169 A023170 A023171 this_sequence A023173 A023174 A023175
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KEYWORD
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nonn
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AUTHOR
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David W. Wilson (davidwwilson(AT)comcast.net)
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EXTENSIONS
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Edited by Don Reble (djr(AT)nk.ca), Sep 07 2003
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