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

%I A368179 #13 Dec 21 2023 03:06:18
%S A368179 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 A368179 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 A368179 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 A368179 Square array read by ascending antidiagonals: row n is the trajectory of n under the A006368 map.
%H A368179 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 A368179 <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%e A368179 Array begins:
%e A368179   [ 0]   0,  0,  0,  0,  0,  0,  0,  0,  0,  0,  0, ... = A000004
%e A368179   [ 1]   1,  1,  1,  1,  1,  1,  1,  1,  1,  1,  1, ... = A000012
%e A368179   [ 2]   2,  3,  2,  3,  2,  3,  2,  3,  2,  3,  2, ... = A010693
%e A368179   [ 3]   3,  2,  3,  2,  3,  2,  3,  2,  3,  2,  3, ... = A176059
%e A368179   [ 4]   4,  6,  9,  7,  5,  4,  6,  9,  7,  5,  4, ... = A180853
%e A368179   [ 5]   5,  4,  6,  9,  7,  5,  4,  6,  9,  7,  5, ... = A180853 (shifted)
%e A368179   [ 6]   6,  9,  7,  5,  4,  6,  9,  7,  5,  4,  6, ... = A180853 (shifted)
%e A368179   [ 7]   7,  5,  4,  6,  9,  7,  5,  4,  6,  9,  7, ... = A180853 (shifted)
%e A368179   [ 8]   8, 12, 18, 27, 20, 30, 45, 34, 51, 38, 57, ... = A028393
%e A368179   [ 9]   9,  7,  5,  4,  6,  9,  7,  5,  4,  6,  9, ... = A180853 (shifted)
%e A368179   [10]  10, 15, 11,  8, 12, 18, 27, 20, 30, 45, 34, ... = A180864 (shifted)
%e A368179   ...    |   |   |
%e A368179       A001477|A168221
%e A368179              |
%e A368179           A006368
%t A368179 A006368[n_]:=If[OddQ[n],Floor[(3n+2)/4],3n/2];
%t A368179 A368179list[dmax_]:=With[{a=Reverse[Table[NestList[A006368,n-1,dmax-n],{n,dmax}]]},Array[Diagonal[a,#]&,dmax,1-dmax]];
%t A368179 A368179list[15] (* Generates 15 antidiagonals *)
%Y A368179 Rows: A000004, A000012, A010693,  A028393, A028395, A094332, A176059, A180853, A180864, A182205, A217218, A223086, A223087, A223088.
%Y A368179 Columns: A001477, A006368, A168221.
%Y A368179 Main diagonal: A368180.
%K A368179 nonn,tabl,easy
%O A368179 0,4
%A A368179 _Paolo Xausa_, Dec 15 2023