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A220237 Triangle read by rows: sorted terms of Collatz trajectories.

%I A220237 #16 Oct 16 2021 19:23:28
%S A220237 1,1,2,1,2,3,4,5,8,10,16,1,2,4,1,2,4,5,8,16,1,2,3,4,5,6,8,10,16,1,2,4,
%T A220237 5,7,8,10,11,13,16,17,20,22,26,34,40,52,1,2,4,8,1,2,4,5,7,8,9,10,11,
%U A220237 13,14,16,17,20,22,26,28,34,40,52,1,2,4,5,8,10,16
%N A220237 Triangle read by rows: sorted terms of Collatz trajectories.
%C A220237 n-th row = sorted list of {A070165(n,k): k = 1..A006577(n)};
%C A220237 T(n,1) = 1 if Collatz conjecture is true.
%H A220237 Reinhard Zumkeller, <a href="/A220237/b220237.txt">Rows n = 1..120 of triangle, flattened</a>
%H A220237 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A220237 The table begins:
%e A220237 .   1:  [1]
%e A220237 .   2:  [1,2]
%e A220237 .   3:  [1,2,3,4,5,8,10,16]
%e A220237 .   4:  [1,2,4]
%e A220237 .   5:  [1,2,4,5,8,16]
%e A220237 .   6:  [1,2,3,4,5,6,8,10,16]
%e A220237 .   7:  [1,2,4,5,7,8,10,11,13,16,17,20,22,26,34,40,52]
%e A220237 .   8:  [1,2,4,8]
%e A220237 .   9:  [1,2,4,5,7,8,9,10,11,13,14,16,17,20,22,26,28,34,40,52]
%e A220237 .  10:  [1,2,4,5,8,10,16]
%e A220237 .  11:  [1,2,4,5,8,10,11,13,16,17,20,26,34,40,52]
%e A220237 .  12:  [1,2,3,4,5,6,8,10,12,16] .
%p A220237 T:= proc(n) option remember; `if`(n=1, 1,
%p A220237       sort([n, T(`if`(n::even, n/2, 3*n+1))])[])
%p A220237     end:
%p A220237 seq(T(n), n=1..10);  # _Alois P. Heinz_, Oct 16 2021
%t A220237 Flatten[Table[Sort[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]],{n,12}]] (* _Harvey P. Dale_, Jan 28 2013 *)
%o A220237 (Haskell)
%o A220237 import Data.List (sort)
%o A220237 a220237 n k = a220237_tabf !! (n-1) !! (k-1)
%o A220237 a220237_row n = a220237_tabf !! (n-1)
%o A220237 a220237_tabf = map sort a070165_tabf
%Y A220237 Cf. A006577 (row lengths), A025586(right edge), A033493 (row sums).
%K A220237 nonn,tabf,look
%O A220237 1,3
%A A220237 _Reinhard Zumkeller_, Jan 03 2013