A355312 Irregular triangle read by rows, in which the rows list groups of consecutive integers taking the same number of halving and tripling steps to reach 1 in '3X+1' problem. Groups are in order of the number of steps required, and in numerical order among those with the same number of steps.

20, 21, 12, 13, 84, 85, 52, 53, 340, 341, 34, 35, 212, 213, 226, 227, 1364, 1365, 68, 69, 70, 452, 453, 454, 22, 23, 140, 141, 150, 151, 852, 853, 908, 909, 5460, 5461, 44, 45, 46, 276, 277, 300, 301, 302, 1812, 1813, 14, 15, 92, 93, 564, 565, 604, 605, 3412, 3413

Offset: 1

Author

Paul Duckett, Jun 27 2022

Keywords

• nonn
• tabf

Examples

			20 and 21 are terms since they both use 7 steps (trajectories 20, 10, 5, 16, 8, 4, 2, 1 and 21, 64, 32, 16, 8, 4, 2, 1).
300, 301 and 302 are terms since they all use 16 steps.
The triangle starts:
   7:  20   21
   9:  12   13   84   85
  11:  52   53  340  341
  13:  34   35  212  213  226  227 1364 1365
  14:  68   69   70  452  453  454
  15:  22   23  140  141  150  151  852  853  908  909 5460 5461
  16:  44   45   46  276  277  300  301  302 1812 1813
  17:  14   15   92   93  564  565  604  605 3412 3413
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..11035
• Rémy Sigrist, PARI program
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Cf. A006577, A078417.

Subtriangle of A127824.

Programs

PARI

See Links section.