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 A336007 Numbers whose mixed Zeckendorf-Lucas representation is not a Zeckendorf or Lucas representation. See Comments. 1
 17, 25, 28, 38, 41, 45, 46, 52, 53, 59, 62, 66, 67, 72, 73, 74, 75, 81, 82, 84, 85, 86, 93, 96, 100, 101, 106, 107, 108, 109, 114, 117, 118, 119, 120, 121, 122, 128, 129, 131, 132, 133, 136, 137, 138, 139, 140, 148, 151, 155, 156, 161, 162, 163, 164, 169 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Suppose that B1 and B2 are increasing sequences of positive integers, and let B be the increasing sequence of numbers in the union of B1 and B2. Every positive integer n has a unique representation given by the greedy algorithm with B1 as base, and likewise for B2 and B. LINKS EXAMPLE 17 = 13 + 4; 25 = 21 + 4; 28 = 21 + 7. MATHEMATICA fibonacciQ[n_] := IntegerQ[Sqrt[5 n^2 + 4]] || IntegerQ[Sqrt[5 n^2 - 4]]; Attributes[fibonacciQ] = {Listable}; lucasQ[n_] := IntegerQ[Sqrt[5 n^2 + 20]] || IntegerQ[Sqrt[5 n^2 - 20]]; Attributes[lucasQ] = {Listable}; s = Reverse[Union[Flatten[Table[{Fibonacci[n + 1], LucasL[n - 1]}, {n, 1, 22}]]]]; u = Map[#[[1]] &, Select[Map[{#[[1]], {Apply[And, fibonacciQ[#[[2]]]], Apply[And, lucasQ[#[[2]]]]}} &, Map[{#, DeleteCases[ s Reap[FoldList[(Sow[Quotient[#1, #2]]; Mod[#1, #2]) &, #, s]][[2, 1]], 0]} &, Range[500]]], #[[2]] == {False, False} &]] (* Peter J. C. Moses, Jun 14 2020 *) CROSSREFS Cf. A007895, A014417, A116543, A214973, A336004. Sequence in context: A124971 A272635 A105448 * A082130 A140609 A131275 Adjacent sequences: A336004 A336005 A336006 * A336008 A336009 A336010 KEYWORD nonn,base AUTHOR Clark Kimberling, Jul 06 2020 STATUS approved

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Last modified January 31 05:53 EST 2023. Contains 359947 sequences. (Running on oeis4.)