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

1,2

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