A050100 -id:A050100 - cp's OEIS frontend

A050101 a(n) is the position of n in A050100.

1, 31, 3, 12, 21, 30, 36, 42, 48, 2, 8, 11, 14, 17, 20, 23, 26, 29, 208, 32, 211, 35, 38, 78, 41, 44, 118, 47, 84, 4, 155, 87, 7, 158, 90, 10, 56, 93, 263, 13, 59, 96, 16, 300, 62, 19, 201, 269, 402, 22, 102, 204, 25, 306, 68, 28, 207, 241, 275

Offset: 1

Clark Kimberling

nonn

Definition corrected by Clark Kimberling, Jul 01 2021

A050102 Numbers k such that A050100(k) < A050100(k+1).

Original entry on oeis.org

1, 3, 4, 8, 12, 14, 17, 21, 23, 26, 31, 32, 36, 38, 42, 44, 48, 49, 50, 56, 59, 62, 64, 68, 71, 74, 78, 79, 84, 87, 90, 93, 96, 97, 102, 103, 108, 111, 114, 118, 119, 120, 121, 127, 132, 135, 138, 141, 142, 147, 151, 155, 158, 160, 163

Offset: 1

Clark Kimberling

nonn

Cf. A050100.

Definition corrected by Georg Fischer, Aug 06 2021

A050103 Numbers k such that A050100(k) > A050100(k+1).

Original entry on oeis.org

2, 5, 6, 7, 9, 10, 11, 13, 15, 16, 18, 19, 20, 22, 24, 25, 27, 28, 29, 30, 33, 34, 35, 37, 39, 40, 41, 43, 45, 46, 47, 51, 52, 53, 54, 55, 57, 58, 60, 61, 63, 65, 66, 67, 69, 70, 72, 73, 75, 76, 77, 80, 81, 82, 83, 85, 86, 88, 89, 91, 92

Offset: 1

Clark Kimberling

nonn

Cf. A050100.

Definition corrected by Georg Fischer, Aug 06 2021

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

A050101 a(n) is the position of n in A050100.

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A050102 Numbers k such that A050100(k) < A050100(k+1).

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Extensions

A050103 Numbers k such that A050100(k) > A050100(k+1).

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Extensions

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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