A375266 Irregular triangle read by rows in which row n lists the iterates of the A375265 map from n to 1.

1, 2, 1, 3, 1, 4, 2, 1, 5, 16, 8, 4, 2, 1, 6, 2, 1, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 8, 4, 2, 1, 9, 3, 1, 10, 5, 16, 8, 4, 2, 1, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1, 12, 4, 2, 1, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1

Offset: 1

Author

Paolo Xausa, Aug 08 2024

Keywords

• nonn
• tabf
• easy

Comments

By definition the trajectory ends when 1 is reached, so row 1 does not contain the cycle 1 -> 4 -> 2 -> 1.

See A375265 for links.

Examples

			Triangle begins:
   1;
   2,  1;
   3,  1;
   4,  2,  1;
   5, 16,  8,  4,  2,  1;
   6,  2,  1;
   7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10,  5, 16,  8,  4,  2,  1;
   8,  4,  2,  1;
   9,  3,  1;
  10,  5, 16,  8,  4,  2,  1;
  ...
		

Links

• Paolo Xausa, Table of n, a(n) for n = 1..12824 (rows 1..300 of the triangle, flattened).
• Index entries for sequences related to 3x+1 (or Collatz) problem.

Crossrefs

Cf. A375265, A375267 (# of iterations), A375268 (row sums), A375280 (row maxs).

Cf. A070165, A070168, A235795, A350279, A350548.

Programs

Mathematica

A375265[n_] := Which[Divisible[n, 3], n/3, Divisible[n, 2], n/2, True, 3*n + 1];
Array[NestWhileList[A375265, #, # > 1 &] &, 15]