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

0,4

Links

Table of n, a(n) for n=0..81.

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

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.

Example

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
  ...

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}]

Crossrefs

Cf. A070165, A349407, A350279, A350515.

Sequence in context: A292978 A202178 A035543 * A105546 A342237 A367267

Adjacent sequences: A350545 A350546 A350547 * A350549 A350550 A350551

Keyword

nonn,easy,tabf

Author

Paolo Xausa, Jan 04 2022

Status

approved