A191453 Dispersion of (2*floor(3*n/2)), by antidiagonals.

1, 2, 3, 6, 8, 4, 18, 24, 12, 5, 54, 72, 36, 14, 7, 162, 216, 108, 42, 20, 9, 486, 648, 324, 126, 60, 26, 10, 1458, 1944, 972, 378, 180, 78, 30, 11, 4374, 5832, 2916, 1134, 540, 234, 90, 32, 13, 13122, 17496, 8748, 3402, 1620, 702, 270, 96, 38, 15, 39366

Offset

1,2

Comments

Background discussion: Suppose that s is an increasing sequence of positive integers, that the complement t of s is infinite, and that t(1)=1. The dispersion of s is the array D whose n-th row is (t(n), s(t(n)), s(s(t(n))), s(s(s(t(n)))), ...). Every positive integer occurs exactly once in D, so that, as a sequence, D is a permutation of the positive integers. The sequence u given by u(n)=(number of the row of D that contains n) is a fractal sequence. Examples:

(1) s=A000040 (the primes), D=A114537, u=A114538.

(2) s=A022343 (without initial 0), D=A035513 (Wythoff array), u=A003603.

(3) s=A007067, D=A035506 (Stolarsky array), u=A133299.

More recent examples of dispersions: A191426-A191455.

Links

Table of n, a(n) for n=1..56.

Example

Northwest corner:
  1...2....6....18...54
  3...8....24...72...216
  4...12...36...108..324
  5...14...42...126..378
  7...20...60...180..540

Mathematica

(* Program generates the dispersion array T of increasing sequence f[n] *)
r=40; r1=12; c=40; c1=12;
f[n_] :=2Floor[3n/2]   (* complement of column 1 *)
mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]
rows = {NestList[f, 1, c]};
Do[rows = Append[rows, NestList[f, mex[Flatten[rows]], r]], {r}];
t[i_, j_] := rows[[i, j]];
TableForm[Table[t[i, j], {i, 1, 10}, {j, 1, 10}]]
(* A191453 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191453 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

Crossrefs

Cf. A114537, A035513, A035506.

Sequence in context: A140266 A140265 A349917 * A191454 A379143 A276955

Adjacent sequences: A191450 A191451 A191452 * A191454 A191455 A191456

Keyword

nonn,tabl

Author

Clark Kimberling, Jun 05 2011

Status

approved