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 A050000 a(n) = floor(a(n-1)/2) if this is not among 0, a(1), ..., a(n-2); otherwise a(n) = 3*a(n-1). 30
 1, 3, 9, 4, 2, 6, 18, 54, 27, 13, 39, 19, 57, 28, 14, 7, 21, 10, 5, 15, 45, 22, 11, 33, 16, 8, 24, 12, 36, 108, 324, 162, 81, 40, 20, 60, 30, 90, 270, 135, 67, 201, 100, 50, 25, 75, 37, 111, 55, 165, 82, 41, 123, 61, 183, 91, 273, 136, 68 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS This permutation of the natural numbers is the multiply-and-divide (MD) sequence for (M,D)=(3,2). The "MD question" is this: for relatively prime M and D, does the MD sequence contain every positive integer exactly once? An affirmative proof for the more general condition that log base D of M is irrational is given by Mateusz Kwaśnicki in Crux Mathematicorum 30 (2004) 235-239. - Clark Kimberling, Jun 30 2004 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Clark Kimberling, Unsolved Problems and Rewards. Mateusz Kwaśnicki, The solution of M-D problem (2008). Index entries for sequences that are permutations of the natural numbers MATHEMATICA a[0] = 0; a[1] = 1; a[n_] := a[n] = (b = Floor[a[n-1]/2]; If[FreeQ[Table[ a[k], {k, 0, n-2}], b], b, 3*a[n-1]]); Array[a, 60] (* Jean-François Alcover, Jul 13 2016 *) PROG (Haskell) a050000 n = a050000_list !! (n-1) a050000_list = 1 : f [1, 0] where f xs'@(x:xs) | x `div` 2 `elem` xs = 3 * x : f (3 * x : xs') | otherwise = x `div` 2 : f (x `div` 2 : xs') -- Reinhard Zumkeller, Nov 13 2011 CROSSREFS Cf. A050076, A050001 (inverse). MD sequences: A050076 (2,3), A050124 (2,5), this sequence (3,2), A050104 (3,4), A050080 (4,3), A050004 (5,2), A050084 (5,3), A050108 (5,4), A050008 (6,2), A050088 (6,3), A050112 (6,4), A050012 (7,2), A050092 (7,3), A050096 (8,3), A050016 (9,2), A050020 (10,2), A050100 (10,3). Sequence in context: A342220 A197507 A264992 * A154368 A321120 A243711 Adjacent sequences: A049997 A049998 A049999 * A050001 A050002 A050003 KEYWORD nonn,nice,easy AUTHOR Clark Kimberling STATUS approved

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Last modified August 4 17:39 EDT 2024. Contains 374923 sequences. (Running on oeis4.)