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

2, 34, 610, 10946, 196418, 3524578, 63245986, 1134903170, 6557470319842, 117669030460994, 37889062373143906, 679891637638612258, 12200160415121876738, 3928413764606871165730, 1264937032042997393488322

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Feb 12 2010

Keywords

• nonn

Comments

See A037918 for an implicit list of the squarefree F.

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..49

Crossrefs

Cf. A000045, A067259, A173207.

Programs

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 *)

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

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