A191544 - OEIS

A191544

Dispersion of (floor(7*n/3)), by antidiagonals.

1, 2, 3, 4, 7, 5, 9, 16, 11, 6, 21, 37, 25, 14, 8, 49, 86, 58, 32, 18, 10, 114, 200, 135, 74, 42, 23, 12, 266, 466, 315, 172, 98, 53, 28, 13, 620, 1087, 735, 401, 228, 123, 65, 30, 15, 1446, 2536, 1715, 935, 532, 287, 151, 70, 35, 17, 3374, 5917, 4001, 2181

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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..59.

EXAMPLE

Northwest corner:

1...2....4....9...21

3...7....16...37..86

5...11...25...58..135

6...14...32...74..172

8...18...42...98..228

MATHEMATICA

(* Program generates the dispersion array T of the complement of increasing sequence f[n] *)

r=40; r1=12; c=40; c1=12; f[n_] :=Floor[7n/3]] (* 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}]]

(* A191544 array *)

Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191544 sequence *)

(* Program by Peter J. C. Moses, Jun 01 2011 *)

CROSSREFS

Cf. A114537, A035513, A035506.

Sequence in context: A257801 A257726 A183089 * A191438 A191730 A233560

Adjacent sequences: A191541 A191542 A191543 * A191545 A191546 A191547

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jun 09 2011

STATUS

approved