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

0,2

Comments

Sequence A176866 gives the length of each row. Sequences A176867 and A176868 give the minimum and maximum number in each row. Observe how each row has clumps of numbers -- a feature evident in the graph. Sequence A221474 counts these clumps.

Links

T. D. Noe, Rows n = 0..40 of triangle, flattened

Example

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.

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]

Crossrefs

Cf. A176866, A176867, A176868.

Cf. A127824 (table of even and odd numbers taking n iterations).

Cf. A221474 (number of clumps).

Sequence in context: A199637 A199636 A324038 * A199638 A296356 A154825

Adjacent sequences: A221470 A221471 A221472 * A221474 A221475 A221476

Keyword

nonn,tabf,look

Author

T. D. Noe, Feb 13 2013

Status

approved