A350548 Irregular triangle T(n,k) read by rows in which row n lists the iterates of the A350515 map from n to 0.

0, 1, 0, 2, 1, 0, 3, 5, 8, 4, 1, 0, 4, 1, 0, 5, 8, 4, 1, 0, 6, 3, 5, 8, 4, 1, 0, 7, 2, 1, 0, 8, 4, 1, 0, 9, 14, 7, 2, 1, 0, 10, 3, 5, 8, 4, 1, 0, 11, 17, 26, 13, 4, 1, 0, 12, 6, 3, 5, 8, 4, 1, 0, 13, 4, 1, 0, 14, 7, 2, 1, 0, 15, 23, 35, 53, 80, 40, 13, 4, 1, 0

Offset: 0

Author

Paolo Xausa, Jan 04 2022

Keywords

• nonn
• easy
• tabf

Examples

			Written as an irregular triangle, the sequence begins:
  n\k   0   1   2   3   4   5   6
  -------------------------------
   0:   0
   1:   1   0
   2:   2   1   0
   3:   3   5   8   4   1   0
   4:   4   1   0
   5:   5   8   4   1   0
   6:   6   3   5   8   4   1   0
   7:   7   2   1   0
   8:   8   4   1   0
   9:   9  14   7   2   1   0
  10:  10   3   5   8   4   1   0
  11:  11  17  26  13   4   1   0
  ...
		

Links

• Emre Yolcu, Scott Aaronson and Marijn J. H. Heule, An Automated Approach to the Collatz Conjecture, arXiv:2105.14697 [cs.LO], 2021, pp. 21-25.
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A070165, A349407, A350279, A350515.

Programs

Mathematica

A350515[n_]:=If[Mod[n,3]==1,(n-1)/3,If[Mod[n,6]==0||Mod[n,6]==2,n/2,(3n+1)/2]];
nrows=20;Table[NestWhileList[A350515,n,#>0&],{n,0, nrows-1}]

Formula

T(n,0) = n; T(n,k) = A350515(T(n,k-1)), where n >= 0 and k >= 1.

T(n,k) = (A350279(n+1,k+1)-1)/2, where n >= 0 and k >= 0.