This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A245691 #12 Nov 17 2019 01:43:50
%S A245691 1,3,2,6,2,6,3,9,5,15,8,24,12,6,4,12,6,5,15,8,24,12,6,6,18,9,5,15,8,
%T A245691 24,12,6,7,21,11,33,17,51,26,78,39,20,60,30,15,8,24,12,6,8,24,12,6,9,
%U A245691 27,14,42,21,11,33,17,51,26,78,39,20,60,30,15,8,24,12
%N A245691 Irregular triangle of Collatz like iteration, x -> 3x, then repeat (x -> ceiling(x/2) if divisible by 3, otherwise x -> 3x) while x != 6.
%C A245691 It is conjectured that the number of steps for the trajectory to arrive at 6 is equal to the number of steps for the Collatz trajectory to arrive at 1 for the same starting value n (n>1), suggesting the length of the n-th row of the irregular array is given by A008908(n). Note that if the starting value of a trajectory in the Collatz sequence is not treated as a potential stopping value, then the conjecture would also be valid for n = 1.
%C A245691 Starting with x the first step in this sequence is always to multiply by 3. Thereafter if x <> 6, divide by 2 (rounding up) if x mod 3 = 0, otherwise multiply by 3. If the initial multiply-by-3 step is omitted the sequence still arrives at 6 for any starting value (conjecturally), but the length of the trajectory would no longer be the same as the length of the Collatz trajectory for starting values (n>1) that are divisible by 3.
%C A245691 While any odd number in the classic Collatz trajectory is immediately followed by an even number, trajectories in this sequence may contain a contiguous run of odd numbers. The trajectory starting with 27 is the lowest with more odd numbers than even numbers in its sequence.
%e A245691 The irregular array a(n,k) starts:
%e A245691 n\k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ...
%e A245691 1: 1 3 2 6
%e A245691 2: 2 6
%e A245691 3: 3 9 5 15 8 24 12 6
%e A245691 4: 4 12 6
%e A245691 5: 5 15 8 24 12 6
%e A245691 6: 6 18 9 5 15 8 24 12 6
%e A245691 7: 7 21 11 33 17 51 26 78 39 20 60 30 15 8 24 12 6
%e A245691 8: 8 24 12 6
%e A245691 9: 9 27 14 42 21 11 33 17 51 26 78 39 20 60 30 15 8 24 12 6
%e A245691 10: 10 30 15 8 24 12 6
%e A245691 11: 11 33 17 51 26 78 39 20 60 30 15 8 24 12 6
%e A245691 12: 12 36 18 9 5 15 8 24 12 6
%e A245691 13: 13 39 20 60 30 15 8 24 12 6
%e A245691 14: 14 42 21 11 33 17 51 26 78 39 20 60 30 15 8 24 12 6
%e A245691 15: 15 45 23 69 35 105 53 159 80 240 120 60 30 15 8 24 12 6
%o A245691 (PARI) { for(n=1, 15, x=n*3; print1(n,", ",x,", "); while(x!=6, if(x%3, x*=3, x=ceil(x/2)); print1(x,", "))) }
%Y A245691 Cf. A008908, A245942.
%K A245691 nonn,tabf
%O A245691 1,2
%A A245691 _K. Spage_, Aug 07 2014