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

0,8

Comments

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

Links

Table of n, a(n) for n=0..69.

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}]

Crossrefs

Sequence in context: A355851 A140302 A085341 * A160812 A338271 A176866

Adjacent sequences: A221471 A221472 A221473 * A221475 A221476 A221477

Keyword

nonn

Author

T. D. Noe, Feb 13 2013

Status

approved