A220237 Triangle read by rows: sorted terms of Collatz trajectories.

1, 1, 2, 1, 2, 3, 4, 5, 8, 10, 16, 1, 2, 4, 1, 2, 4, 5, 8, 16, 1, 2, 3, 4, 5, 6, 8, 10, 16, 1, 2, 4, 5, 7, 8, 10, 11, 13, 16, 17, 20, 22, 26, 34, 40, 52, 1, 2, 4, 8, 1, 2, 4, 5, 7, 8, 9, 10, 11, 13, 14, 16, 17, 20, 22, 26, 28, 34, 40, 52, 1, 2, 4, 5, 8, 10, 16

Offset: 1

Author

Reinhard Zumkeller, Jan 03 2013

Keywords

• nonn
• tabf
• look

Comments

n-th row = sorted list of {A070165(n,k): k = 1..A006577(n)};

T(n,1) = 1 if Collatz conjecture is true.

Examples

			The table begins:
.   1:  [1]
.   2:  [1,2]
.   3:  [1,2,3,4,5,8,10,16]
.   4:  [1,2,4]
.   5:  [1,2,4,5,8,16]
.   6:  [1,2,3,4,5,6,8,10,16]
.   7:  [1,2,4,5,7,8,10,11,13,16,17,20,22,26,34,40,52]
.   8:  [1,2,4,8]
.   9:  [1,2,4,5,7,8,9,10,11,13,14,16,17,20,22,26,28,34,40,52]
.  10:  [1,2,4,5,8,10,16]
.  11:  [1,2,4,5,8,10,11,13,16,17,20,26,34,40,52]
.  12:  [1,2,3,4,5,6,8,10,12,16] .
		

Links

• Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006577 (row lengths), A025586(right edge), A033493 (row sums).

Programs

Haskell

import Data.List (sort)
a220237 n k = a220237_tabf !! (n-1) !! (k-1)
a220237_row n = a220237_tabf !! (n-1)
a220237_tabf = map sort a070165_tabf

Maple

T:= proc(n) option remember; `if`(n=1, 1,
      sort([n, T(`if`(n::even, n/2, 3*n+1))])[])
    end:
seq(T(n), n=1..10);  # Alois P. Heinz, Oct 16 2021

Mathematica

Flatten[Table[Sort[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]],{n,12}]] (* Harvey P. Dale, Jan 28 2013 *)