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).

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

Author

Clark Kimberling

Keywords

• nonn
• nice
• easy

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

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).

Programs

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

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 *)