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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 A355312 #42 Jul 12 2022 08:39:52
%S A355312 20,21,12,13,84,85,52,53,340,341,34,35,212,213,226,227,1364,1365,68,
%T A355312 69,70,452,453,454,22,23,140,141,150,151,852,853,908,909,5460,5461,44,
%U A355312 45,46,276,277,300,301,302,1812,1813,14,15,92,93,564,565,604,605,3412,3413
%N 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.
%H A355312 Rémy Sigrist, <a href="/A355312/b355312.txt">Table of n, a(n) for n = 1..11035</a>
%H A355312 Rémy Sigrist, <a href="/A355312/a355312.gp.txt">PARI program</a>
%H A355312 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A355312 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 A355312 300, 301 and 302 are terms since they all use 16 steps.
%e A355312 The triangle starts:
%e A355312    7:  20   21
%e A355312    9:  12   13   84   85
%e A355312   11:  52   53  340  341
%e A355312   13:  34   35  212  213  226  227 1364 1365
%e A355312   14:  68   69   70  452  453  454
%e A355312   15:  22   23  140  141  150  151  852  853  908  909 5460 5461
%e A355312   16:  44   45   46  276  277  300  301  302 1812 1813
%e A355312   17:  14   15   92   93  564  565  604  605 3412 3413
%o A355312 (PARI) See Links section.
%Y A355312 Cf. A006577, A078417.
%Y A355312 Subtriangle of A127824.
%K A355312 nonn,tabf
%O A355312 1,1
%A A355312 _Paul Duckett_, Jun 27 2022