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A191541 Dispersion of (2*floor(n*sqrt(2))), by antidiagonals. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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..57.

EXAMPLE

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

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_] :=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 *)

CROSSREFS

Cf. A114537, A035513, A035506, A191540.

Sequence in context: A320504 A181799 A137623 * A122398 A329567 A326487

Adjacent sequences:  A191538 A191539 A191540 * A191542 A191543 A191544

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jun 07 2011

STATUS

approved

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Last modified April 4 05:34 EDT 2020. Contains 333212 sequences. (Running on oeis4.)