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

Author

Clark Kimberling, Jan 02 2021

Keywords

• nonn
• tabl

Comments

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.

Examples

			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
		

Crossrefs

Cf. A191450, A333029, A340244.

Programs

Mathematica

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 *)