A191540 -id:A191540 - cp's OEIS frontend

1, 2, 3, 4, 8, 5, 10, 22, 14, 6, 28, 62, 38, 16, 7, 78, 174, 106, 44, 18, 9, 220, 492, 298, 124, 50, 24, 11, 622, 1390, 842, 350, 140, 66, 30, 12, 1758, 3930, 2380, 988, 394, 186, 84, 32, 13, 4972, 11114, 6730, 2794, 1114, 526, 236, 90, 36, 15, 14062, 31434

Offset: 1

Clark Kimberling, Jun 07 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...2....4....10...28
  3...8....22...62...174
  5...14...38...106..298
  6...16...44...124..350
  7...18...50...140..394

Cf. A114537, A035513, A035506, A191540.

(* Program generates the dispersion array T of the complement of increasing sequence f[n] *)
r=40; r1=12; c=40; c1=12; f[n_] :=2*Floor[n*Sqrt[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}]]
(* A191541 array *)
Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191541 sequence *)
(* Program by Peter J. C. Moses, Jun 01 2011 *)

cp's OEIS Frontend

A191541 Dispersion of (2floor(nsqrt(2))), by antidiagonals.

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