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A191455 Dispersion of (floor(n*e)), by antidiagonals. 41
1, 2, 3, 5, 8, 4, 13, 21, 10, 6, 35, 57, 27, 16, 7, 95, 154, 73, 43, 19, 9, 258, 418, 198, 116, 51, 24, 11, 701, 1136, 538, 315, 138, 65, 29, 12, 1905, 3087, 1462, 856, 375, 176, 78, 32, 14, 5178, 8391, 3974, 2326, 1019, 478, 212, 86, 38, 15, 14075, 22809 (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....5....13...35

3...8....21...57...154

4...10...27...73...198

6...16...43...116..315

7...19...51...138..375

MAPLE

A191455 := proc(r, c)

    option remember;

    if c = 1 then

        A054385(r) ;

    else

        A022843(procname(r, c-1)) ;

    end if;

end proc: # R. J. Mathar, Jan 25 2015

MATHEMATICA

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

r=40; r1=12; c=40; c1=12;

f[n_] :=Floor[n*E]   (* 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}]]

(* A191455 array *)

Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A191455 sequence *)

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

CROSSREFS

Cf. A114537, A035513, A035506.

Sequence in context: A105836 A105822 A191543 * A191540 A191450 A257122

Adjacent sequences:  A191452 A191453 A191454 * A191456 A191457 A191458

KEYWORD

nonn,tabl

AUTHOR

Clark Kimberling, Jun 05 2011

STATUS

approved

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Last modified March 30 18:37 EDT 2020. Contains 333127 sequences. (Running on oeis4.)