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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
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
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
KEYWORD
nonn,nice,easy
STATUS
approved