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 A333029 Order array of array A333028, read by antidiagonals. 3
 1, 2, 4, 3, 6, 10, 5, 8, 15, 11, 7, 12, 24, 18, 13, 9, 19, 38, 28, 21, 16, 14, 30, 58, 45, 32, 25, 17, 22, 47, 77, 65, 50, 40, 27, 20, 35, 67, 95, 84, 70, 60, 44, 31, 23, 55, 86, 112, 102, 89, 79, 64, 49, 36, 26, 74, 104, 128, 118, 106, 97, 83, 69, 56, 43 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Suppose that (r(n,k)), for n >=1 and k >= 1 is an array of distinct numbers.  Replace each r(n,k) by its position when all the numbers r(n,k) are ordered by <.  The resulting array is the order array of (r(n,k)).  The array A333029 is an interspersion and, as a sequence, a permutation of the natural numbers. REFERENCES Clark Kimberling, "Fractal sequences and interspersions," Ars Combinatoria 45 (1997) 157-168. LINKS Clark Kimberling, Lucas Representations of Positive Integers, J. Int. Seq., Vol. 23 (2020), Article 20.9.5. EXAMPLE Northwest corner:    1   2   3   5   7    9   14   22    4   6   8  12  19   30   47   67   10  15  24  38  58   77   95  112   11  18  24  45  65   84  102  118   13  21  32  50  70   89  106  122   16  25  40  60  79   97  114  130   17  27  44  64  83  101  117  132 MATHEMATICA W[n_, k_] := Fibonacci[k + 1] Floor[n*GoldenRatio] + (n - 1) Fibonacci[k]; t = Table[GCD[W[n, 1], W[n, 2]], {n, 1, 500}]; u = Flatten[Position[t, 1]] ; v[n_, k_] := W[u[[n]], k]; g = Sort[Table[v[n - k + 1, k], {n, 20}, {k, n, 1, -1}] // Flatten] wo[n_, k_] := Length[Intersection[Range[v[n, k]], Complement[Range, g]]] WP[n_, k_] := v[n, k] - wo[n, k]; TableForm[Table[WP[n, k], {n, 1, 15}, {k, 1, 10}]]  (* A333029 array *) Table[WP[n - k + 1, k], {n, 16}, {k, n, 1, -1}] // Flatten  (* A333029 sequence *) CROSSREFS Cf. A333028. Sequence in context: A113233 A051849 A283961 * A175498 A318452 A083673 Adjacent sequences:  A333026 A333027 A333028 * A333030 A333031 A333032 KEYWORD nonn,tabl AUTHOR Clark Kimberling, Mar 10 2020 STATUS approved

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Last modified May 15 16:02 EDT 2021. Contains 343920 sequences. (Running on oeis4.)