login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A232666 6-free Fibonacci numbers. 3
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 4, 93, 97, 190, 287, 477, 764, 1241, 2005, 541, 2546, 3087, 5633, 8720, 14353, 23073, 37426, 60499, 97925, 26404, 124329, 150733, 275062, 425795, 700857, 1126652, 1827509, 2954161, 796945, 3751106, 4548051, 8299157, 12847208, 21146365, 33993573 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

The sequences of n-free Fibonacci numbers were suggested by John H. Conway.

a(n) is the sum of the two previous terms divided by the largest possible power of 6.

4-free Fibonacci numbers are A224382.

The sequence coincides with the Fibonacci sequence until the first multiple of 6 in the Fibonacci sequence: 144, which in this sequence is divided by 36 to produce 4.

7-free Fibonacci numbers is A078414.

LINKS

Table of n, a(n) for n=0..46.

B. Avila, T. Khovanova, Free Fibonacci Sequences, J. Int. Seq. 17 (2014) # 14.8.5.

MATHEMATICA

sixPower[n_] := (a = Transpose[FactorInteger[n]]; a2 = Position[a[[1]], 2]; a3 = Position[a[[1]], 3]; If[Length[a2] == 0 || Length[a3] == 0 , res = 0, res = Min[a[[2]][[a2[[1]][[1]]]], a[[2]][[a3[[1]][[1]]]]]]; res); sixFree[n_] := n/6^sixPower[n]; appendNext6Free[list_] := Append[list, sixFree[list[[-1]] + list[[-2]]]]; Nest[appendNext6Free, {0, 1}, 50]

CROSSREFS

Cf. A224382, A214684.

Sequence in context: A132634 A096275 A093089 * A093091 A105471 A189722

Adjacent sequences: A232663 A232664 A232665 * A232667 A232668 A232669

KEYWORD

nonn

AUTHOR

Brandon Avila and Tanya Khovanova, Nov 27 2013

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified December 9 04:13 EST 2022. Contains 358698 sequences. (Running on oeis4.)