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

1,2

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)

Links

Table of n, a(n) for n=1..66.

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

Example

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

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 *)

Crossrefs

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

Sequence in context: A075375 A191670 A065562 * A233342 A120233 A265667

Adjacent sequences: A272901 A272902 A272903 * A272905 A272906 A272907

Keyword

nonn,tabl,easy

Author

Clark Kimberling, May 10 2016

Status

approved