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A220237 Triangle read by rows: sorted terms of Collatz trajectories. 6

%I #16 Oct 16 2021 19:23:28

%S 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 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 13,14,16,17,20,22,26,28,34,40,52,1,2,4,5,8,10,16

%N Triangle read by rows: sorted terms of Collatz trajectories.

%C n-th row = sorted list of {A070165(n,k): k = 1..A006577(n)};

%C T(n,1) = 1 if Collatz conjecture is true.

%H Reinhard Zumkeller, <a href="/A220237/b220237.txt">Rows n = 1..120 of triangle, flattened</a>

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%e The table begins:

%e . 1: [1]

%e . 2: [1,2]

%e . 3: [1,2,3,4,5,8,10,16]

%e . 4: [1,2,4]

%e . 5: [1,2,4,5,8,16]

%e . 6: [1,2,3,4,5,6,8,10,16]

%e . 7: [1,2,4,5,7,8,10,11,13,16,17,20,22,26,34,40,52]

%e . 8: [1,2,4,8]

%e . 9: [1,2,4,5,7,8,9,10,11,13,14,16,17,20,22,26,28,34,40,52]

%e . 10: [1,2,4,5,8,10,16]

%e . 11: [1,2,4,5,8,10,11,13,16,17,20,26,34,40,52]

%e . 12: [1,2,3,4,5,6,8,10,12,16] .

%p T:= proc(n) option remember; `if`(n=1, 1,

%p sort([n, T(`if`(n::even, n/2, 3*n+1))])[])

%p end:

%p seq(T(n), n=1..10); # _Alois P. Heinz_, Oct 16 2021

%t Flatten[Table[Sort[NestWhileList[If[EvenQ[#],#/2,3#+1]&,n,#>1&]],{n,12}]] (* _Harvey P. Dale_, Jan 28 2013 *)

%o (Haskell)

%o import Data.List (sort)

%o a220237 n k = a220237_tabf !! (n-1) !! (k-1)

%o a220237_row n = a220237_tabf !! (n-1)

%o a220237_tabf = map sort a070165_tabf

%Y Cf. A006577 (row lengths), A025586(right edge), A033493 (row sums).

%K nonn,tabf,look

%O 1,3

%A _Reinhard Zumkeller_, Jan 03 2013

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Last modified August 17 18:09 EDT 2024. Contains 375227 sequences. (Running on oeis4.)