A368179 Square array read by ascending antidiagonals: row n is the trajectory of n under the A006368 map.

0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 6, 3, 3, 1, 0, 6, 4, 9, 2, 2, 1, 0, 7, 9, 6, 7, 3, 3, 1, 0, 8, 5, 7, 9, 5, 2, 2, 1, 0, 9, 12, 4, 5, 7, 4, 3, 3, 1, 0, 10, 7, 18, 6, 4, 5, 6, 2, 2, 1, 0, 11, 15, 5, 27, 9, 6, 4, 9, 3, 3, 1, 0, 12, 8, 11, 4, 20, 7, 9, 6, 7, 2, 2, 1, 0

Offset

0,4

Links

Paolo Xausa, Table of n, a(n) for n = 0..11324 (antidiagonals 1..150 of the array, flattened).

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

Array begins:
  [ 0]   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, ... = A000004
  [ 1]   1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ... = A000012
  [ 2]   2,  3,  2,  3,  2,  3,  2,  3,  2,  3,  2, ... = A010693
  [ 3]   3,  2,  3,  2,  3,  2,  3,  2,  3,  2,  3, ... = A176059
  [ 4]   4,  6,  9,  7,  5,  4,  6,  9,  7,  5,  4, ... = A180853
  [ 5]   5,  4,  6,  9,  7,  5,  4,  6,  9,  7,  5, ... = A180853 (shifted)
  [ 6]   6,  9,  7,  5,  4,  6,  9,  7,  5,  4,  6, ... = A180853 (shifted)
  [ 7]   7,  5,  4,  6,  9,  7,  5,  4,  6,  9,  7, ... = A180853 (shifted)
  [ 8]   8, 12, 18, 27, 20, 30, 45, 34, 51, 38, 57, ... = A028393
  [ 9]   9,  7,  5,  4,  6,  9,  7,  5,  4,  6,  9, ... = A180853 (shifted)
  [10]  10, 15, 11,  8, 12, 18, 27, 20, 30, 45, 34, ... = A180864 (shifted)
  ...    |   |   |
      A001477|A168221
             |
          A006368

Mathematica

A006368[n_]:=If[OddQ[n], Floor[(3n+2)/4], 3n/2];
A368179list[dmax_]:=With[{a=Reverse[Table[NestList[A006368, n-1, dmax-n], {n, dmax}]]}, Array[Diagonal[a, #]&, dmax, 1-dmax]];
A368179list[15] (* Generates 15 antidiagonals *)

Crossrefs

Rows: A000004, A000012, A010693, A028393, A028395, A094332, A176059, A180853, A180864, A182205, A217218, A223086, A223087, A223088.

Columns: A001477, A006368, A168221.

Main diagonal: A368180.

Sequence in context: A216216 A078803 A368227 * A130403 A130402 A089840

Adjacent sequences: A368176 A368177 A368178 * A368180 A368181 A368182

Keyword

nonn,tabl,easy

Author

Paolo Xausa, Dec 15 2023

Status

approved