

A232666


6free 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
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OFFSET

0,4


COMMENTS

The sequences of nfree 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.
4free 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.
7free Fibonacci numbers is A078414.


LINKS



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



STATUS

approved



