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

1,2

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.

Links

Table of n, a(n) for n=1..63.

Example

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

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 *)

Crossrefs

Cf. A191450, A333029, A340244.

Sequence in context: A266285 A258851 A194031 * A064357 A191735 A191666

Adjacent sequences: A340242 A340243 A340244 * A340246 A340247 A340248

Keyword

nonn,tabl

Author

Clark Kimberling, Jan 02 2021

Status

approved