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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 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

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