A221474 Number of families of numbers requiring n iterations of the Collatz (3x+1) function to reach 1.

1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 3, 3, 4, 4, 5, 4, 6, 5, 6, 5, 7, 6, 7, 7, 8, 7, 9, 8, 9, 9, 10, 10, 11, 10, 11, 11, 12, 11, 13, 12, 13, 13, 14, 14, 15, 14, 16, 15, 16, 16, 17, 17, 18, 17, 18, 18, 19, 19, 20, 19, 21, 20, 22, 21, 23, 22, 24

Offset: 0

Author

T. D. Noe, Feb 13 2013

Keywords

• nonn

Comments

Looking at the graph of A221473, it is apparent that the numbers requiring n iterations clump into families.

Programs

Mathematica

nn = 41; s = {1}; t = Join[s, Table[s = Union[2 s, (Select[s, Mod[#, 3] == 1 && OddQ[(# - 1)/3] && (# - 1)/3 > 1 &] - 1)/3]; s, {n, nn-1}]]; t2 = Join[{{t[[1]]}}, Table[Select[t[[i]], OddQ], {i, 2, nn}]]; Table[t3 = t2[[n]]; If[Length[t3] <= 1, Length[t3], s = Round[Rest[t3]/Most[t3]]; Length[Select[s, # > 1 &]] + 1], {n, nn}]