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A272908 Rectangular array, by antidiagonals: row n give the positions of n in the Lucas-products fractal sequence, A272907.

%I A272908 #5 May 14 2016 13:56:14
%S A272908 1,2,5,3,7,8,4,10,11,16,6,13,14,20,23,9,17,18,25,28,35,12,21,22,30,33,
%T A272908 41,46,15,26,27,36,39,48,53,62,19,31,32,42,45,55,60,70,77,24,37,38,49,
%U A272908 52,63,68,79,86,97,29,43,44,56,59,71,76,88,95,107,116
%N A272908 Rectangular array, by antidiagonals:  row n give the positions of n in the Lucas-products fractal sequence, A272907.
%C A272908 This array is an interspersion.  Every positive integer occurs exactly once, and each row is interspersed by each other row, except for initial terms.
%e A272908 Northwest corner:
%e A272908 1     2     3     4     6     9     12    15
%e A272908 5     7     10    13    17    21    26    31
%e A272908 8     11    14    18    22    27    32    38
%e A272908 16    20    25    30    36    42    49    56
%e A272908 23    28    33    39    45    52    59    67
%e A272908 35    41    48    55    63    71    80    89
%e A272908 46    53    60    68    76    85    94    104
%t A272908 z = 500; f[n_] := LucasL[n]; u1 = Table[f[n], {n, 1, z}];
%t A272908 u2 = Sort[Flatten[Table[f[i]*f[j], {i, 1, z}, {j, i, z}]]];
%t A272908 uf = Table[Select[Range[80], MemberQ[u1, u2[[i]]/f[#]] &][[1]], {i, 1, z}]
%t A272908 r[n_, k_] := Flatten[Position[uf, n]][[k]]
%t A272908 TableForm[Table[r[n, k], {n, 1, 12}, {k, 1, 12}]]  (* A272908 array *)
%t A272908 Table[r[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (* A272908 sequence *)
%Y A272908 Cf. A000032, A272907, A272909, A272904 (Fibonacci-products interspersion).
%K A272908 nonn,tabl,easy
%O A272908 1,2
%A A272908 _Clark Kimberling_, May 10 2016