A340244 -id:A340244 - cp's OEIS frontend

A340245 Order array of the Wythoff B-array (A340244): an interspersion, read by antidiagonals.

1, 2, 4, 3, 7, 5, 6, 11, 9, 8, 10, 19, 15, 14, 12, 17, 31, 26, 23, 20, 13, 28, 51, 43, 39, 32, 22, 16, 46, 81, 71, 64, 53, 36, 27, 18, 75, 110, 101, 94, 83, 60, 44, 30, 21, 105, 138, 130, 123, 112, 90, 73, 49, 35, 24, 133, 165, 157, 151, 140, 119, 103, 79

Offset: 1

Clark Kimberling, Jan 02 2021

Suppose that (r(n,k)), for n >= 1 and k >= 1 is an array of distinct numbers. Replace each r(n,k) with its position when all the numbers r(n,k) are ordered by <. The resulting array is the order array of (r(n,k)). The order array A340245 is an interspersion and a dispersion, and, as a sequence, a permutation of the natural numbers; see A333029 and A191450.

			Corner:
   1    2    3    6   10    17    28    46
   4    7   11   19   31    51    81   110
   5    9   15   26   43    71   101   130
   8   14   23   39   64    94   123   151
  12   20   32   53   83   112   140   167

Cf. A191450, A333029, A340244.

r = GoldenRatio; f[n_] := Fibonacci[n];
a[n_] := Floor[r*n]; b[n_] := Floor[r^2*n];
c[n_] := a[a[b[n]]]; d[n_] := b[a[b[n]]];
w[n_, k_] := f[k - 2] c[n] + f[k - 1] d[n];
Grid[Table[w[n, k], {n, 1, 9}, {k, 1, 15}]] (* A340244 array *)
u = Table[w[n - k + 1, k], {n, 30}, {k, n, 1, -1}]//Flatten  (* A340244 sequence *)
rk[n_] := Position[Sort[u], u[[n]]];
Take[Flatten[Table[rk[n], {n, 1, 350}]], 100]  (* A340245 sequence *)

cp's OEIS Frontend

A340245 Order array of the Wythoff B-array (A340244): an interspersion, read by antidiagonals.

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