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%I #8 Mar 24 2017 00:47:55
%S 1,2,3,4,5,8,10,16,6,7,11,13,17,20,22,26,34,40,52,9,14,28,12,15,23,35,
%T 46,53,70,80,106,160,18,19,29,44,58,88,21,32,64,24,25,38,76,27,31,41,
%U 47,61,62,71,82,91,92,94,103,107,121,122,124,137,142,155,161
%N Irregular triangle of numbers first appearing in the Collatz (3x+1) iteration of n.
%C Sequence A222118 gives the number of terms in each row.
%H T. D. Noe, <a href="/A222297/b222297.txt">Rows n = 1..4000 of irregular triangle, flattened</a>
%e The irregular table begins
%e {1},
%e {2},
%e {3, 4, 5, 8, 10, 16},
%e {},
%e {},
%e {6},
%e {7, 11, 13, 17, 20, 22, 26, 34, 40, 52},
%e {},
%e {9, 14, 28},
%e {},
%e {},
%e {12},
%e {},
%e {},
%e {15, 23, 35, 46, 53, 70, 80, 106, 160}
%t Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; found = {}; t = Table[c = Collatz[n]; r = Complement[c, found]; found = Union[found, c]; r, {n, 27}]; Flatten[t]
%Y Cf. A222118.
%K nonn,tabf
%O 1,2
%A _T. D. Noe_, Feb 23 2013
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