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A191442 Dispersion of ([n*sqrt(3)+1/2]), where [ ]=floor, by antidiagonals. 4
1, 2, 4, 3, 7, 6, 5, 12, 10, 8, 9, 21, 17, 14, 11, 16, 36, 29, 24, 19, 13, 28, 62, 50, 42, 33, 23, 15, 48, 107, 87, 73, 57, 40, 26, 18, 83, 185, 151, 126, 99, 69, 45, 31, 20, 144, 320, 262, 218, 171, 120, 78, 54, 35, 22, 249, 554, 454, 378, 296, 208, 135, 94 (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..63.

EXAMPLE

Northwest corner:

1....2....3....5...9

4....7....12...21..36

6....10...17...29..50

8....14...24...42..73

11...19...33...57..99

MATHEMATICA

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

r=40; r1=12; c=40; c1=12;  x = Sqr[3];

f[n_] := Floor[n*x+1/2] (* 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}]]

(* A191442 array *)

Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191442 sequence *)

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

CROSSREFS

Cf. A114537, A035513, A035506.

Sequence in context: A199535 A064274 A035513 * A191738 A218602 A114537

Adjacent sequences:  A191439 A191440 A191441 * A191443 A191444 A191445

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jun 04 2011

STATUS

approved

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Last modified February 18 03:43 EST 2018. Contains 299298 sequences. (Running on oeis4.)