A221473 Irregular table of odd numbers whose n-th row has numbers taking n iterations of the Collatz (3x+1) function to reach 1.
1, 5, 3, 21, 13, 85, 53, 341, 17, 113, 35, 213, 227, 1365, 11, 69, 75, 453, 23, 141, 151, 853, 909, 5461, 7, 45, 277, 301, 1813, 15, 93, 565, 605, 3413, 3637, 21845, 29, 181, 201, 1109, 1137, 1205, 7253, 7281, 9, 61, 369, 373, 401, 403, 2261, 2275, 2417
Offset: 0
Examples
Rows 0 to 18 are
{1}
{}
{}
{}
{}
{5}
{}
{3, 21}
{}
{13, 85}
{}
{53, 341}
{17, 113}
{35, 213, 227, 1365}
{11, 69, 75, 453}
{23, 141, 151, 853, 909, 5461}
{7, 45, 277, 301, 1813}
{15, 93, 565, 605, 3413, 3637, 21845}
{29, 181, 201, 1109, 1137, 1205, 7253, 7281}
...
Note that row 18 has 4 clumps: 29, 181-201, 1109-1205, and 7253-7281.
Links
- T. D. Noe, Rows n = 0..40 of triangle, flattened
Crossrefs
Programs
-
Mathematica
nn = 21; 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}]]; Select[Flatten[t], OddQ]
Comments