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A173208 Squarefree Fibonacci numbers F such that F+1 and F-1 are also squarefree.

%I A173208 #19 Oct 02 2024 16:48:49
%S A173208 2,34,610,10946,196418,3524578,63245986,1134903170,6557470319842,
%T A173208 117669030460994,37889062373143906,679891637638612258,
%U A173208 12200160415121876738,3928413764606871165730,1264937032042997393488322
%N A173208 Squarefree Fibonacci numbers F such that F+1 and F-1 are also squarefree.
%C A173208 See A037918 for an implicit list of the squarefree F.
%H A173208 Chai Wah Wu, <a href="/A173208/b173208.txt">Table of n, a(n) for n = 1..49</a>
%t A173208 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
%t A173208 Select[Fibonacci[Range[200]],And@@SquareFreeQ/@{#-1,#,#+1}&] (* _Harvey P. Dale_, Nov 14 2011 *)
%o A173208 (Python)
%o A173208 from sympy import factorint
%o A173208 A173208_list = [2]
%o A173208 a, b = 2, 3
%o A173208 for _ in range(10**2):
%o A173208     if max(factorint(b).values()) <= 1 and max(factorint(b-1).values()) <= 1 and max(factorint(b+1).values()) <= 1:
%o A173208         A173208_list.append(b)
%o A173208     a, b = b, a + b # _Chai Wah Wu_, Jun 08 2015
%Y A173208 Cf. A000045, A067259, A173207.
%K A173208 nonn
%O A173208 1,1
%A A173208 _Vladimir Joseph Stephan Orlovsky_, Feb 12 2010
%E A173208 Description simplified by _R. J. Mathar_, Feb 15 2010
%E A173208 Initial term 2 added, since 1 by convention is squarefree (see A005117) by _Harvey P. Dale_, Nov 15 2011