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A221473
Irregular table of odd numbers whose n-th 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
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.
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. A127824 (table of even and odd numbers taking n iterations).
Cf. A221474 (number of clumps).
Sequence in context: A199637 A199636 A324038 * A199638 A296356 A091593
KEYWORD
nonn,tabf,look
AUTHOR
T. D. Noe, Feb 13 2013
STATUS
approved