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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
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
Sequence in context: A132634 A096275 A093089 * A093091 A105471 A189722
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified June 17 15:57 EDT 2024. Contains 373463 sequences. (Running on oeis4.)