A347271 Irregular triangle T(n,k) read by rows in which row n lists the terms of the 3x+1 trajectory of n, but the row ends when a term is a power of 2 or when a term is less than n, with n >= 1 and k >= 0.

1, 2, 3, 10, 5, 16, 4, 5, 16, 6, 3, 7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 8, 9, 28, 14, 7, 10, 5, 11, 34, 17, 52, 26, 13, 40, 20, 10, 12, 6, 13, 40, 20, 10, 14, 7, 15, 46, 23, 70, 35, 106, 53, 160, 80, 40, 20, 10, 16, 17, 52, 26, 13, 18, 9, 19, 58, 29, 88, 44, 22, 11

Offset: 1

Author

Omar E. Pol, Aug 25 2021

Keywords

• nonn
• tabf

Comments

Note that every row ends when it is easy to know the next missing terms because they are powers of 2 or the last term and the next missing terms form a row that it is already in the sequence.

For a square array with infinitely many terms in every row, see A347270, which is a supersequence that contains all 3x+1 sequences.

Examples

			Triangle begins:
   1;
   2;
   3,  10,   5,  16;
   4;
   5,  16;
   6,   3;
   7,  22,  11,  34,  17,  52,  26,  13,  40,  20,  10,   5;
   8;
   9,  28,  14,   7;
  10,   5;
  11,  34,  17,  52,  26,  13,  40,  20,  10;
  12,   6;
  13,  40,  20,  10;
  14,   7;
  15,  46,  23,  70,  35, 106,  53, 160,  80,  40,  20,  10;
  16;
  17,  52,  26,  13;
  18,   9;
  19,  58,  29,  88,  44,  22,  11;
...
For n = 3 the 3x+1 trajectory is 3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, ... The fourth term is 16 which is a power of 2 so the third row of the triangle is [3, 10, 5, 16].
For n = 6 the 3x+1 trajectory is 6, 3, 10, 5, 16, 8, 4, 2, 1, 4, 2, 1, ... The second term is 3 which is less than 6 so the 6th row of the triangle is [6, 3].
		

Links

• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Subsequence of A070165, of A235795 and of A347270.

Cf. A000079, A006370, A014682, A056959, A235800, A263716.