A272908 - OEIS

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

(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.

LINKS

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

EXAMPLE

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

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 *)

CROSSREFS

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

Sequence in context: A078383 A232644 A125512 * A191432 A135587 A191671

Adjacent sequences: A272905 A272906 A272907 * A272909 A272910 A272911

KEYWORD

nonn,tabl,easy

AUTHOR

Clark Kimberling, May 10 2016

STATUS

approved