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A272904 Rectangular array, by antidiagonals: row n gives the positions of n in the Fibonacci-products fractal sequence, A272900. 3
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 (list; table; graph; refs; listen; history; text; internal format)
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

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Last modified July 25 20:28 EDT 2021. Contains 346291 sequences. (Running on oeis4.)