A191439 -id:A191439 - cp's OEIS frontend

A191440 Dispersion of ([n*sqrt(2)+n+3/2]), where [ ]=floor, by antidiagonals.

1, 3, 2, 8, 6, 4, 20, 15, 11, 5, 49, 37, 28, 13, 7, 119, 90, 69, 32, 18, 9, 288, 218, 168, 78, 44, 23, 10, 696, 527, 407, 189, 107, 57, 25, 12, 1681, 1273, 984, 457, 259, 139, 61, 30, 14, 4059, 3074, 2377, 1104, 626, 337, 148, 73, 35, 16, 9800, 7422, 5740

Offset: 1

Clark Kimberling, Jun 04 2011

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.

			Northwest corner:
  1....3....8....20...49
  2....6....15...37...90
  4....11...28...69...168
  5....13...32...78...189
  7....18...44...107..259

Cf. A114537, A035513, A035506, A191438, A191439, A083087.

(* Program generates the dispersion array T of increasing sequence f[n] *)
r=40; r1=12; c=40; c1=12;  x = Sqr[2];
f[n_] := Floor[n*x+n+3/2] (* 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}]]
(* A191440 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191440 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

cp's OEIS Frontend

A191440 Dispersion of ([n*sqrt(2)+n+3/2]), where [ ]=floor, by antidiagonals.

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