A272904 Rectangular array, by antidiagonals: row n gives the positions of n in the Fibonacci-products fractal sequence, A272900.

1, 2, 4, 3, 6, 8, 5, 9, 11, 15, 7, 12, 14, 19, 23, 10, 16, 18, 24, 28, 34, 13, 20, 22, 29, 33, 40, 46, 17, 25, 27, 35, 39, 47, 53, 61, 21, 30, 32, 41, 45, 54, 60, 69, 77, 26, 36, 38, 48, 52, 62, 68, 78, 86, 96, 31, 42, 44, 55, 59, 70, 76, 87, 95, 106, 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.

Row 1: A033638 (quarter-squares plus 1)

Row 2: A002620 (quarter-squares)

Column 1: A267682 (conjectured)

Examples

			Northwest corner:
1     2     3     4     6     9     12    15
5     7     10    13    17    21    26    31
8     11    14    18    2     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
		

Links

• Clark Kimberling, Orderings of products of Fibonacci numbers, Fibonacci Quarterly 42:1 (2004), pp. 28-35.

Crossrefs

Cf. A000045, A272900, A033638, A002620, A267682, A272908 (Lucas-products interspersion).

Programs

Mathematica

z = 500; f[n_] := Fibonacci[n + 1]; 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}]]  (* A272904 array *)
t = Table[r[n - k + 1, k], {n, 12}, {k, n, 1, -1}] // Flatten (* A272904 sequence *)