A050004 -id:A050004 - cp's OEIS frontend

A050005 a(n) = position of n in A050004.

1, 3, 9, 15, 2, 8, 11, 14, 27, 4, 30, 7, 33, 66, 10, 36, 13, 59, 26, 16, 72, 29, 105, 52, 6, 75, 32, 65, 161, 55, 22, 35, 184, 121, 12, 164, 58, 25, 48, 38, 187, 124, 71, 114, 28, 220, 104, 51, 94, 5, 190, 74, 243, 180, 31, 64, 107, 286, 160

Offset: 1

Clark Kimberling

Cf. A050004.

A050006 Numbers k such that A050004(k) < A050004(k+1).

Original entry on oeis.org

1, 3, 4, 9, 11, 15, 16, 17, 22, 27, 30, 33, 36, 38, 39, 40, 48, 52, 55, 59, 60, 66, 67, 72, 75, 76, 80, 83, 87, 89, 94, 97, 100, 105, 107, 110, 114, 116, 121, 124, 125, 129, 132, 135, 138, 143, 145, 149, 152, 155, 161, 164, 165, 166

Offset: 1

Clark Kimberling

A050007 Numbers k such that A050004(k) > A050004(k+1).

Original entry on oeis.org

2, 5, 6, 7, 8, 10, 12, 13, 14, 18, 19, 20, 21, 23, 24, 25, 26, 28, 29, 31, 32, 34, 35, 37, 41, 42, 43, 44, 45, 46, 47, 49, 50, 51, 53, 54, 56, 57, 58, 61, 62, 63, 64, 65, 68, 69, 70, 71, 73, 74, 77, 78, 79, 81, 82, 84, 85, 86, 88, 90, 91

Offset: 1

Clark Kimberling

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 *)

A050416 a(1)=a(2)=1, then a(n+1) = floor(a(n)/3) if this is not among 0, a(1), ..., a(n); otherwise a(n+1) = a(n) + a(n-1).

Original entry on oeis.org

1, 1, 2, 3, 5, 8, 13, 4, 17, 21, 7, 28, 9, 37, 12, 49, 16, 65, 81, 27, 108, 36, 144, 48, 192, 64, 256, 85, 341, 113, 454, 151, 50, 201, 67, 22, 89, 29, 118, 39, 157, 52, 209, 69, 23, 92, 30, 10, 40, 50, 90, 140, 46, 15, 61, 20, 6, 26, 32

Offset: 1

Clark Kimberling

nonn

Numbers appearing among the terms more than once include 1, 50, 265, 341, 516, 570, 622, ... - Ivan Neretin, Sep 04 2015

Ivan Neretin, Table of n, a(n) for n = 1..10000

Cf. A050417.

Cf. A050000, A050004, A050076, A050080, A050084, A050104, A050124, A050128, A050132, A050135, A050136, A050137, A050138, A050139, A050170, A050196.

a = {0, 1, 1}; Do[AppendTo[a, If[MemberQ[a, c = Quotient[a[[-1]], 3]], a[[-1]] + a[[-2]], c]], {n, 3, 59}]; Delete[a, 1] (* Ivan Neretin, Sep 04 2015 *)

A050137 a(1)=2; a(n) = floor(a(n-1)/2) if this is not among 0,a(1),...,a(n-1); otherwise a(n) = 2*n.

Original entry on oeis.org

2, 1, 6, 3, 10, 5, 14, 7, 18, 9, 4, 24, 12, 28, 30, 15, 34, 17, 8, 40, 20, 44, 22, 11, 50, 25, 54, 27, 13, 60, 62, 31, 66, 33, 16, 72, 36, 76, 38, 19, 82, 41, 86, 43, 21, 92, 46, 23, 98, 49, 102, 51, 106, 53, 26, 112, 56, 116, 58, 29, 122, 61

Offset: 1

Clark Kimberling

Does this sequence contain every positive integer exactly once?

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A050000, A050004, A050128, A050132, A050135, A050136, A050138, A050196.

R:= 2: S:= {2}: a:= 2:
for n from 2 to 100 do
  t:= floor(a/2);
  if t <> 0 and not member(t,S) then a:= t else a:= 2*n fi;
  R:= R,a; S:= S union {a};
od:
R; # Robert Israel, Aug 03 2025

cp's OEIS Frontend

A050005 a(n) = position of n in A050004.

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A050006 Numbers k such that A050004(k) < A050004(k+1).

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A050007 Numbers k such that A050004(k) > A050004(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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Haskell

Mathematica

A050416 a(1)=a(2)=1, then a(n+1) = floor(a(n)/3) if this is not among 0, a(1), ..., a(n); otherwise a(n+1) = a(n) + a(n-1).

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Mathematica

A050137 a(1)=2; a(n) = floor(a(n-1)/2) if this is not among 0,a(1),...,a(n-1); otherwise a(n) = 2*n.

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Maple