A386625 Rectangular array R, read by descending antidiagonals: (row m) = increasing sequence of numbers m*F(n), n>=2, without duplicates, where F = A000045 (Fibonacci numbers); see Comments.
1, 2, 4, 3, 6, 9, 5, 10, 15, 12, 8, 16, 24, 20, 25, 13, 26, 39, 32, 40, 18, 21, 42, 63, 52, 65, 30, 7, 34, 68, 102, 84, 105, 48, 14, 64, 55, 110, 165, 136, 170, 78, 35, 104, 27, 89, 178, 267, 220, 275, 126, 56, 168, 45, 50, 144, 288, 432, 356, 445, 204, 91, 272, 72, 80, 11
Offset: 1
Examples
Corner: 1 2 3 5 8 13 21 34 55 4 6 10 16 26 42 68 110 178 9 15 24 39 63 102 165 267 432 12 20 32 52 84 136 220 356 576 25 40 65 105 170 275 445 720 1165 18 30 48 78 126 204 330 534 864 7 14 35 56 91 147 238 385 623 64 104 168 272 440 712 1152 864 3016 27 45 72 117 189 306 495 801 1296 50 80 130 210 340 550 890 1440 2330 11 22 33 88 143 231 374 605 979 36 60 96 156 252 408 660 1068 1728 Row 4 is obtained from 4*(row 1) by removing 4 and 8.
Programs
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Mathematica
ClearAll[rArray] rArray[rows_, cols_] := Module[{fibs, R = {}, used = <||>, row, val, f, m}, fibs = Map[Fibonacci, Range[2, cols + rows]]; Table[row = {}; Do[val = m*f; If[! KeyExistsQ[used, val], AppendTo[row, val]; used[val] = True;], {f, fibs}]; Take[row, cols], {m, rows}]]; Grid[rArray[16, 12], Frame -> All] (* array *) r[m_, n_] := rArray[12, 12][[m]][[n]]; Table[r[n - k + 1, k], {n, 1, 12}, {k, n, 1, -1}] // Flatten (*sequence*) (* Peter J. C. Moses, Jul 27 2025 *)
Formula
(row 1) = (1,2,3,5,8,13,...) = Fibonacci numbers, {F(n), n>=2}, and for m>1,
(row m) = numbers m*F(n) that are not h*F(k) for any h=2.
Comments