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A238329 Fibonacci numbers that have no prime factors of the form 4k+1. 0
1, 1, 2, 3, 8, 21, 144, 987, 46368, 2178309, 4807526976 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
These are Fibonacci numbers of order 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, and 48. It is somewhat surprising that these are only these Fibonacci numbers having this property.
LINKS
Florian Luca and Lawrence Somer, Lucas sequences for which 4 | phi(abs(u_n)) for almost all n, Fibonacci Quarterly, 44 (2006), pp. 249-262.
MATHEMATICA
Join[{1, 1}, Select[Fibonacci[Range[200]], Union[Mod[Transpose[FactorInteger[#]][[1]], 4]][[1]] > 1 &]]
npfQ[n_]:=Count[FactorInteger[n][[All, 1]], _?(Mod[#, 4]==1&)]==0; Join[ {1, 1}, Select[ Fibonacci[Range[50]], npfQ]] (* Harvey P. Dale, Jun 15 2019 *)
CROSSREFS
Cf. A000045 (Fibonacci numbers).
Sequence in context: A004790 A245464 A243562 * A272333 A098119 A049959
KEYWORD
nonn,fini,full
AUTHOR
T. D. Noe, Feb 26 2014
STATUS
approved

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Last modified April 23 18:16 EDT 2024. Contains 371916 sequences. (Running on oeis4.)