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 A220237 Triangle read by rows: sorted terms of Collatz trajectories. 6
 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, 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, 13, 14, 16, 17, 20, 22, 26, 28, 34, 40, 52, 1, 2, 4, 5, 8, 10, 16 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,3 COMMENTS n-th row = sorted list of {A070165(n,k): k = 1..A006577(n)}; T(n,1) = 1 if Collatz conjecture is true. LINKS Reinhard Zumkeller, Rows n = 1..120 of triangle, flattened Index entries for sequences related to 3x+1 (or Collatz) problem EXAMPLE The table begins: . 1: [1] . 2: [1,2] . 3: [1,2,3,4,5,8,10,16] . 4: [1,2,4] . 5: [1,2,4,5,8,16] . 6: [1,2,3,4,5,6,8,10,16] . 7: [1,2,4,5,7,8,10,11,13,16,17,20,22,26,34,40,52] . 8: [1,2,4,8] . 9: [1,2,4,5,7,8,9,10,11,13,14,16,17,20,22,26,28,34,40,52] . 10: [1,2,4,5,8,10,16] . 11: [1,2,4,5,8,10,11,13,16,17,20,26,34,40,52] . 12: [1,2,3,4,5,6,8,10,12,16] . MAPLE T:= proc(n) option remember; `if`(n=1, 1, sort([n, T(`if`(n::even, n/2, 3*n+1))])[]) end: seq(T(n), n=1..10); # Alois P. Heinz, Oct 16 2021 MATHEMATICA Flatten[Table[Sort[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&]], {n, 12}]] (* Harvey P. Dale, Jan 28 2013 *) PROG (Haskell) import Data.List (sort) a220237 n k = a220237_tabf !! (n-1) !! (k-1) a220237_row n = a220237_tabf !! (n-1) a220237_tabf = map sort a070165_tabf CROSSREFS Cf. A006577 (row lengths), A025586(right edge), A033493 (row sums). Sequence in context: A057045 A237753 A058700 * A050040 A277282 A191973 Adjacent sequences: A220234 A220235 A220236 * A220238 A220239 A220240 KEYWORD nonn,tabf,look AUTHOR Reinhard Zumkeller, Jan 03 2013 STATUS approved

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Last modified December 2 04:12 EST 2023. Contains 367506 sequences. (Running on oeis4.)