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

1,1

Comments

See A037918 for an implicit list of the squarefree F.

Links

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

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

Cf. A000045, A067259, A173207.

Sequence in context: A045585 A092883 A134495 * A344107 A361773 A224882

Adjacent sequences: A173205 A173206 A173207 * A173209 A173210 A173211

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, Feb 12 2010

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