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

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, 41, 46, 15, 26, 27, 36, 39, 48, 53, 62, 19, 31, 32, 42, 45, 55, 60, 70, 77, 24, 37, 38, 49, 52, 63, 68, 79, 86, 97, 29, 43, 44, 56, 59, 71, 76, 88, 95, 107, 116

Offset: 1

Author

Clark Kimberling, May 10 2016

Keywords

• nonn
• tabl
• easy

Comments

This array is an interspersion. Every positive integer occurs exactly once, and each row is interspersed by each other row, except for initial terms.

Examples

			Northwest corner:
1     2     3     4     6     9     12    15
5     7     10    13    17    21    26    31
8     11    14    18    22    27    32    38
16    20    25    30    36    42    49    56
23    28    33    39    45    52    59    67
35    41    48    55    63    71    80    89
46    53    60    68    76    85    94    104
		

Crossrefs

Cf. A000032, A272907, A272909, A272904 (Fibonacci-products interspersion).

Programs

Mathematica

z = 500; f[n_] := LucasL[n]; u1 = Table[f[n], {n, 1, z}];
u2 = Sort[Flatten[Table[f[i]*f[j], {i, 1, z}, {j, i, z}]]];
uf = Table[Select[Range[80], MemberQ[u1, u2[[i]]/f[#]] &][[1]], {i, 1, z}]
r[n_, k_] := Flatten[Position[uf, n]][[k]]
TableForm[Table[r[n, k], {n, 1, 12}, {k, 1, 12}]]  (* A272908 array *)
Table[r[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten  (* A272908 sequence *)