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A272908
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Rectangular array, by antidiagonals: row n give the positions of n in the Lucas-products fractal sequence, A272907.
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3
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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
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OFFSET
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1,2
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COMMENTS
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This array is an interspersion. Every positive integer occurs exactly once, and each row is interspersed by each other row, except for initial terms.
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LINKS
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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