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A050000
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a(n)=[ a(n-1)/2 ] if this is not among 0,a(1),...,a(n-2), else a(n)=3*a(n-1).
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5
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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; internal format)
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OFFSET
| 1,2
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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 (ck6(AT)evansville.edu), Jun 30 2004
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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
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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
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CROSSREFS
| Cf. A050076, A050001 (inverse).
Sequence in context: A200012 A130701 A197507 * A154368 A161773 A021721
Adjacent sequences: A049997 A049998 A049999 * A050001 A050002 A050003
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KEYWORD
| nonn,nice,easy
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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