|
%I #16 Jan 29 2014 08:33:23
%S 1,5,3,21,13,85,53,341,17,113,35,213,227,1365,11,69,75,453,23,141,151,
%T 853,909,5461,7,45,277,301,1813,15,93,565,605,3413,3637,21845,29,181,
%U 201,1109,1137,1205,7253,7281,9,61,369,373,401,403,2261,2275,2417
%N Irregular table of odd numbers whose n-th row has numbers taking n iterations of the Collatz (3x+1) function to reach 1.
%C 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.
%H T. D. Noe, <a href="/A221473/b221473.txt">Rows n = 0..40 of triangle, flattened</a>
%e Rows 0 to 18 are
%e {1}
%e {}
%e {}
%e {}
%e {}
%e {5}
%e {}
%e {3, 21}
%e {}
%e {13, 85}
%e {}
%e {53, 341}
%e {17, 113}
%e {35, 213, 227, 1365}
%e {11, 69, 75, 453}
%e {23, 141, 151, 853, 909, 5461}
%e {7, 45, 277, 301, 1813}
%e {15, 93, 565, 605, 3413, 3637, 21845}
%e {29, 181, 201, 1109, 1137, 1205, 7253, 7281}
%e ...
%e Note that row 18 has 4 clumps: 29, 181-201, 1109-1205, and 7253-7281.
%t 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]
%Y Cf. A176866, A176867, A176868.
%Y Cf. A127824 (table of even and odd numbers taking n iterations).
%Y Cf. A221474 (number of clumps).
%K nonn,tabf,look
%O 0,2
%A _T. D. Noe_, Feb 13 2013
|
