A050096 -id:A050096 - cp's OEIS frontend

A050097 a(n)=position of n in A050096.

1, 3, 11, 8, 5, 19, 16, 2, 33, 10, 53, 27, 7, 24, 70, 4, 145, 18, 64, 272, 15, 61, 295, 12, 58, 292, 81, 32, 55, 367, 78, 9, 286, 52, 75, 205, 26, 335, 49, 6, 228, 23, 358, 46, 69, 199, 251, 20, 381, 43, 144, 196, 248, 300, 352, 17, 115, 63

Offset: 1

Clark Kimberling

nonn

A050098 Numbers k such that A050096(k) < A050096(k+1).

Original entry on oeis.org

1, 3, 5, 8, 11, 12, 16, 19, 20, 24, 27, 28, 33, 34, 35, 39, 43, 46, 49, 53, 55, 58, 61, 64, 65, 70, 71, 75, 78, 81, 82, 83, 84, 90, 94, 97, 100, 101, 104, 109, 111, 115, 116, 117, 122, 123, 129, 132, 133, 138, 140, 145, 146, 148, 152

Offset: 1

Clark Kimberling

nonn

A050099 Numbers k such that A050096(k) > A050096(k+1).

Original entry on oeis.org

2, 4, 6, 7, 9, 10, 13, 14, 15, 17, 18, 21, 22, 23, 25, 26, 29, 30, 31, 32, 36, 37, 38, 40, 41, 42, 44, 45, 47, 48, 50, 51, 52, 54, 56, 57, 59, 60, 62, 63, 66, 67, 68, 69, 72, 73, 74, 76, 77, 79, 80, 85, 86, 87, 88, 89, 91, 92, 93, 95, 96

Offset: 1

Clark Kimberling

nonn

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).

Original entry on oeis.org

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

Clark Kimberling

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

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

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).

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

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 *)

cp's OEIS Frontend

A050097 a(n)=position of n in A050096.

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A050098 Numbers k such that A050096(k) < A050096(k+1).

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A050099 Numbers k such that A050096(k) > A050096(k+1).

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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).

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