

A221473


Irregular table of odd numbers whose nth row has numbers taking n iterations of the Collatz (3x+1) function to reach 1.


2



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
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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, 181201, 11091205, and 72537281.


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



