A176866
The number of odd numbers that require n Collatz (3x+1) iterations to reach 1.
Original entry on oeis.org
1, 0, 0, 0, 0, 1, 0, 2, 0, 2, 0, 2, 2, 4, 4, 6, 5, 7, 8, 14, 14, 19, 22, 30, 36, 48, 60, 79, 94, 118, 154, 194, 248, 315, 390, 486, 623, 792, 1008, 1261, 1579, 2007, 2555, 3219, 4043, 5109, 6464, 8204, 10351, 13100, 16575, 20889, 26398, 33388, 42155, 53370, 67414
Offset: 0
23, 141, 151, 853, 909, and 5461 are the only odd numbers that require exactly 15 iterations to reach 1. Hence a(15)=6.
At row 15 with a(16) = 5 nodes 4 (mod 6) the left-right symmetry for the number of 4 (mod 6) nodes in the Collatz tree A127824 is broken for the first time: in the left half of the tree there are the three nodes 22, 136 and 832 but on the right half only the two nodes 904 and 5440. - _Wolfdieter Lang_, Mar 26 2014
Cf.
A005186 (number of numbers having stopping time n).
Cf.
A127824 (numbers having stopping time n).
A176868
Greatest odd number that requires n Collatz (3x+1) iterations to reach 1, or zero if there is no such number.
Original entry on oeis.org
1, 0, 0, 0, 0, 5, 0, 21, 0, 85, 0, 341, 113, 1365, 453, 5461, 1813, 21845, 7281, 87381, 29125, 349525, 116501, 1398101, 466033, 5592405, 1864133, 22369621, 7456533, 89478485, 29826161, 357913941, 119304645, 1431655765, 477218581, 5726623061, 1908874353
Offset: 0
-
nn = 10; t1 = {0, 0, 5, 21, 85, 341, 1365}; Do[AppendTo[t1, 4 t1[[-1]] + 1], {3*nn}]; t2 = {1, 0, 0, 0, 0, 0, 113}; Do[AppendTo[t2, 4 t2[[-1]] + 1]; AppendTo[t2, 4 t2[[-1]] + 1]; AppendTo[t2, 4 t2[[-1]] + 29], {nn}]; t = Riffle[t2, t1] (* T. D. Noe, Feb 14 2013 *)
A221473
Irregular table of odd numbers whose n-th row has numbers taking n iterations of the Collatz (3x+1) function to reach 1.
Original entry on oeis.org
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
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.
Cf.
A127824 (table of even and odd numbers taking n iterations).
-
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]
Showing 1-3 of 3 results.
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