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A272908 Rectangular array, by antidiagonals: row n give the positions of n in the Lucas-products fractal sequence, A272907. 3
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
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
KEYWORD
nonn,tabl,easy
AUTHOR
Clark Kimberling, May 10 2016
STATUS
approved

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Last modified March 28 18:04 EDT 2024. Contains 371254 sequences. (Running on oeis4.)