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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 Table of n, a(n) for n=1..11. 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 Adjacent sequences: A238326 A238327 A238328 * A238330 A238331 A238332 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.)