%I #13 Nov 02 2021 13:30:30
%S 0,1,2,4,5,7,6,9,10,11,11,13,12,4,5,1,6,3,2,4,7,8,9,8,10,11,9,13,11,
%T 13,12,14,15,5,16,16,6,18,17,20,17,19,7,4,5,4,6,1,5,6,7,7,2,9,6,8,7,
%U 17,18,9,19,9,10,20,20,11,10,22,11,24,21,23,21,36,37
%N Triangle read by rows giving trajectory of k/(2n+1) in Collatz problem, k = 1..2n.
%C Extension of A210483 with negative values, and subset of A224360.
%e The 2nd row [4, 5, 7, 6] gives the number of iterations of k/5 (the first element is not counted):
%e k=1 => 1/5 >2/5 > 1/5 > 8/5 > 4/5 with 4 iterations;
%e k=2 => 2/5 > 1/5 > 2/5 > 1/5 > 8/5 > 4/5 with 5 iterations;
%e k=3 => 3/5 > 4/5 > 2/5 > 1/5 > 2/5 > 1/5 > 8/5 > 4/5 with 7 iterations;
%e k=4 => 4/5 > 2/5 > 1/5 > 2/5 > 1/5 > 8/5 > 4/5 with 6 iterations.
%e The array starts:
%e [0];
%e [1, 2];
%e [4, 5, 7, 6];
%e [9, 10, 11, 11, 13, 12];
%e [4, 5, 1, 6, 3, 2, 4, 7];
%e ...
%t Collatz[n_] := NestWhileList[If[EvenQ[Numerator[#]], #/2, 3 # + 1] &, n, UnsameQ, All]; t = Join[{{0}}, Table[s = Collatz[k/(2*n + 1)]; len = Length[s]  2; If[s[[1]] == 2, len = len  1]; len, {n, 10}, {k, 2*n}]]; Flatten[t] (* program from _T. D. Noe_, adapted for this sequence  see A210483 *).
%Y Cf. A210483, A210468, A224299, A224360.
%K nonn,tabf
%O 0,3
%A _Michel Lagneau_, Apr 05 2013
