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

%I A368227 #14 Dec 21 2023 05:25:06
%S A368227 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,
%T A368227 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,
%U A368227 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
%N A368227 Square array read by ascending antidiagonals: row n is the trajectory of n under the A006369 map.
%H A368227 Paolo Xausa, <a href="/A368227/b368227.txt">Table of n, a(n) for n = 0..11324</a> (antidiagonals 1..150 of the array, flattened).
%H A368227 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A368227 Array begins:
%e A368227   [ 0]   0,  0,  0,  0,  0,  0,  0,  0,  0,   0,  0, ... = A000004
%e A368227   [ 1]   1,  1,  1,  1,  1,  1,  1,  1,  1,   1,  1, ... = A000012
%e A368227   [ 2]   2,  3,  2,  3,  2,  3,  2,  3,  2,   3,  2, ... = A010693
%e A368227   [ 3]   3,  2,  3,  2,  3,  2,  3,  2,  3,   2,  3, ... = A176059
%e A368227   [ 4]   4,  5,  7,  9,  6,  4,  5,  7,  9,   6,  4, ... = A094328
%e A368227   [ 5]   5,  7,  9,  6,  4,  5,  7,  9,  6,   4,  5, ... = A094328 (shifted)
%e A368227   [ 6]   6,  4,  5,  7,  9,  6,  4,  5,  7,   9,  6, ... = A094328 (shifted)
%e A368227   [ 7]   7,  9,  6,  4,  5,  7,  9,  6,  4,   5,  7, ... = A094328 (shifted)
%e A368227   [ 8]   8, 11, 15, 10, 13, 17, 23, 31, 41,  55, 73, ... = A028394
%e A368227   [ 9]   9,  6,  4,  5,  7,  9,  6,  4,  5,   7,  9, ... = A094328 (shifted)
%e A368227   [10]  10, 13, 17, 23, 31, 41, 55, 73, 97, 129, 86, ... = A028394 (shifted)
%e A368227   ...    |   |   |
%e A368227       A001477|A168222
%e A368227           A006369
%t A368227 A006369[n_]:=If[Divisible[n,3],2n/3,Round[4n/3]];
%t A368227 A368227list[dmax_]:=With[{a=Reverse[Table[NestList[A006369,n-1,dmax-n],{n,dmax}]]},Array[Diagonal[a,#]&,dmax,1-dmax]];
%t A368227 A368227list[15] (* Generates 15 antidiagonals *)
%Y A368227 Rows: A000004, A000012, A010693, A028394, A028396, A094328, A094329, A176059, A185589, A185590, A217729, A223083, A223084, A223085.
%Y A368227 Columns: A001477, A006369, A168222.
%Y A368227 Main diagonal: A368228.
%Y A368227 Cf. A368179.
%K A368227 nonn,tabl,easy
%O A368227 0,4
%A A368227 _Paolo Xausa_, Dec 18 2023