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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 September 10 02:58 EDT 2024. Contains 375770 sequences. (Running on oeis4.)