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Square array read by ascending antidiagonals: row n is the trajectory of n under the A006368 map.
4

%I #13 Dec 21 2023 03:06:18

%S 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,

%T 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,

%U 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

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

%H Paolo Xausa, <a href="/A368179/b368179.txt">Table of n, a(n) for n = 0..11324</a> (antidiagonals 1..150 of the array, flattened).

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

%e Array begins:

%e [ 0] 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, ... = A000004

%e [ 1] 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, ... = A000012

%e [ 2] 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, ... = A010693

%e [ 3] 3, 2, 3, 2, 3, 2, 3, 2, 3, 2, 3, ... = A176059

%e [ 4] 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, ... = A180853

%e [ 5] 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, 5, ... = A180853 (shifted)

%e [ 6] 6, 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, ... = A180853 (shifted)

%e [ 7] 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, 7, ... = A180853 (shifted)

%e [ 8] 8, 12, 18, 27, 20, 30, 45, 34, 51, 38, 57, ... = A028393

%e [ 9] 9, 7, 5, 4, 6, 9, 7, 5, 4, 6, 9, ... = A180853 (shifted)

%e [10] 10, 15, 11, 8, 12, 18, 27, 20, 30, 45, 34, ... = A180864 (shifted)

%e ... | | |

%e A001477|A168221

%e |

%e A006368

%t A006368[n_]:=If[OddQ[n],Floor[(3n+2)/4],3n/2];

%t A368179list[dmax_]:=With[{a=Reverse[Table[NestList[A006368,n-1,dmax-n],{n,dmax}]]},Array[Diagonal[a,#]&,dmax,1-dmax]];

%t A368179list[15] (* Generates 15 antidiagonals *)

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

%Y Columns: A001477, A006368, A168221.

%Y Main diagonal: A368180.

%K nonn,tabl,easy

%O 0,4

%A _Paolo Xausa_, Dec 15 2023