A368227 Square array read by ascending antidiagonals: row n is the trajectory of n under the A006369 map.

0, 1, 0, 2, 1, 0, 3, 3, 1, 0, 4, 2, 2, 1, 0, 5, 5, 3, 3, 1, 0, 6, 7, 7, 2, 2, 1, 0, 7, 4, 9, 9, 3, 3, 1, 0, 8, 9, 5, 6, 6, 2, 2, 1, 0, 9, 11, 6, 7, 4, 4, 3, 3, 1, 0, 10, 6, 15, 4, 9, 5, 5, 2, 2, 1, 0, 11, 13, 4, 10, 5, 6, 7, 7, 3, 3, 1, 0, 12, 15, 17, 5, 13, 7, 4, 9, 9, 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,  5,  7,  9,  6,  4,  5,  7,  9,   6,  4, ... = A094328
  [ 5]   5,  7,  9,  6,  4,  5,  7,  9,  6,   4,  5, ... = A094328 (shifted)
  [ 6]   6,  4,  5,  7,  9,  6,  4,  5,  7,   9,  6, ... = A094328 (shifted)
  [ 7]   7,  9,  6,  4,  5,  7,  9,  6,  4,   5,  7, ... = A094328 (shifted)
  [ 8]   8, 11, 15, 10, 13, 17, 23, 31, 41,  55, 73, ... = A028394
  [ 9]   9,  6,  4,  5,  7,  9,  6,  4,  5,   7,  9, ... = A094328 (shifted)
  [10]  10, 13, 17, 23, 31, 41, 55, 73, 97, 129, 86, ... = A028394 (shifted)
  ...    |   |   |
      A001477|A168222
          A006369

Mathematica

A006369[n_]:=If[Divisible[n, 3], 2n/3, Round[4n/3]];
A368227list[dmax_]:=With[{a=Reverse[Table[NestList[A006369, n-1, dmax-n], {n, dmax}]]}, Array[Diagonal[a, #]&, dmax, 1-dmax]];
A368227list[15] (* Generates 15 antidiagonals *)

Crossrefs

Rows: A000004, A000012, A010693, A028394, A028396, A094328, A094329, A176059, A185589, A185590, A217729, A223083, A223084, A223085.

Columns: A001477, A006369, A168222.

Main diagonal: A368228.

Cf. A368179.

Sequence in context: A186904 A216216 A078803 * A368179 A130403 A130402

Adjacent sequences: A368224 A368225 A368226 * A368228 A368229 A368230

Keyword

nonn,tabl,easy

Author

Paolo Xausa, Dec 18 2023

Status

approved