

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. 249262.


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



