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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 (list; graph; refs; listen; history; text; internal format)
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 A224882 A227935

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

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Last modified November 27 16:20 EST 2021. Contains 349394 sequences. (Running on oeis4.)