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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.

%I A347271 #59 Jan 21 2022 05:06:42
%S A347271 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,
%T A347271 7,10,5,11,34,17,52,26,13,40,20,10,12,6,13,40,20,10,14,7,15,46,23,70,
%U A347271 35,106,53,160,80,40,20,10,16,17,52,26,13,18,9,19,58,29,88,44,22,11
%N 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.
%C A347271 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.
%C A347271 For a square array with infinitely many terms in every row, see A347270, which is a supersequence that contains all 3x+1 sequences.
%H A347271 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A347271 Triangle begins:
%e A347271    1;
%e A347271    2;
%e A347271    3,  10,   5,  16;
%e A347271    4;
%e A347271    5,  16;
%e A347271    6,   3;
%e A347271    7,  22,  11,  34,  17,  52,  26,  13,  40,  20,  10,   5;
%e A347271    8;
%e A347271    9,  28,  14,   7;
%e A347271   10,   5;
%e A347271   11,  34,  17,  52,  26,  13,  40,  20,  10;
%e A347271   12,   6;
%e A347271   13,  40,  20,  10;
%e A347271   14,   7;
%e A347271   15,  46,  23,  70,  35, 106,  53, 160,  80,  40,  20,  10;
%e A347271   16;
%e A347271   17,  52,  26,  13;
%e A347271   18,   9;
%e A347271   19,  58,  29,  88,  44,  22,  11;
%e A347271 ...
%e A347271 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].
%e A347271 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].
%Y A347271 Subsequence of A070165, of A235795 and of A347270.
%Y A347271 Cf. A000079, A006370, A014682, A056959, A235800, A263716.
%K A347271 nonn,tabf
%O A347271 1,2
%A A347271 _Omar E. Pol_, Aug 25 2021