

A340245


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


2



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
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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



