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A173208
Squarefree Fibonacci numbers F such that F+1 and F-1 are also squarefree.
1
2, 34, 610, 10946, 196418, 3524578, 63245986, 1134903170, 6557470319842, 117669030460994, 37889062373143906, 679891637638612258, 12200160415121876738, 3928413764606871165730, 1264937032042997393488322
OFFSET
1,1
COMMENTS
See A037918 for an implicit list of the squarefree F.
LINKS
MATHEMATICA
f[n_]:=Union[Last/@FactorInteger[n]][[ -1]]; lst={}; Do[fibo=Fibonacci[n]; If[f[fibo-1]==1&&f[fibo+1]==1&&f[fibo]==1, AppendTo[lst, fibo]], {n, 4, 200}]; lst
Select[Fibonacci[Range[200]], And@@SquareFreeQ/@{#-1, #, #+1}&] (* Harvey P. Dale, Nov 14 2011 *)
PROG
(Python)
from sympy import factorint
A173208_list = [2]
a, b = 2, 3
for _ in range(10**2):
if max(factorint(b).values()) <= 1 and max(factorint(b-1).values()) <= 1 and max(factorint(b+1).values()) <= 1:
A173208_list.append(b)
a, b = b, a + b # Chai Wah Wu, Jun 08 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
EXTENSIONS
Description simplified by R. J. Mathar, Feb 15 2010
Initial term 2 added, since 1 by convention is squarefree (see A005117) by Harvey P. Dale, Nov 15 2011
STATUS
approved