A355312 - OEIS

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.

%I #42 Jul 12 2022 08:39:52

%S 20,21,12,13,84,85,52,53,340,341,34,35,212,213,226,227,1364,1365,68,

%T 69,70,452,453,454,22,23,140,141,150,151,852,853,908,909,5460,5461,44,

%U 45,46,276,277,300,301,302,1812,1813,14,15,92,93,564,565,604,605,3412,3413

%N 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.

%H Rémy Sigrist, <a href="/A355312/b355312.txt">Table of n, a(n) for n = 1..11035</a>

%H Rémy Sigrist, <a href="/A355312/a355312.gp.txt">PARI program</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%e 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).

%e 300, 301 and 302 are terms since they all use 16 steps.

%e The triangle starts:

%e 7: 20 21

%e 9: 12 13 84 85

%e 11: 52 53 340 341

%e 13: 34 35 212 213 226 227 1364 1365

%e 14: 68 69 70 452 453 454

%e 15: 22 23 140 141 150 151 852 853 908 909 5460 5461

%e 16: 44 45 46 276 277 300 301 302 1812 1813

%e 17: 14 15 92 93 564 565 604 605 3412 3413

%o (PARI) See Links section.

%Y Cf. A006577, A078417.

%Y Subtriangle of A127824.

%K nonn,tabf

%O 1,1

%A _Paul Duckett_, Jun 27 2022