Irregular triangle of numbers that have the same length Collatz (3x+1) iteration.
1, 2, 4, 8, 5, 16, 3, 10, 32, 6, 20, 21, 64, 12, 13, 40, 42, 128, 24, 26, 80, 84, 85, 256, 17, 48, 52, 53, 160, 168, 170, 512, 11, 34, 35, 96, 104, 106, 113, 320, 336, 340, 341, 1024, 7, 22, 23, 68, 69, 70, 75, 192, 208, 212, 213, 226, 227, 640, 672, 680, 682, 2048
1
Each irregular row ends in a power of 2. If a number x appears in a row, then 2x appears in the next row.
Sequence A199636 is this sequence without 1 and the even numbers. - T. D. Noe, Oct 01 2014
T. D. Noe, Plot of 21 irregular rows
T. D. Noe, Table of 21 irregular rows
(Mma) Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, (3*# + 1)/2] &, n, # > 1 &]; nn = 11; c = Table[Length[Collatz[n]], {n, 2^(nn - 1)}]; Flatten[Table[Flatten[Position[c, n]], {n, nn}]]
nonn,tabf,nice
T. D. Noe, Sep 23 2014