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
KEYWORD
nonn
AUTHOR
Brandon Avila and Tanya Khovanova, Nov 27 2013
STATUS
approved