A248514 - OEIS

A248514

Fractal sequence of the dispersion of the "odious numbers".

1, 1, 1, 2, 1, 3, 4, 2, 1, 5, 6, 3, 7, 4, 2, 8, 1, 9, 10, 5, 11, 6, 3, 12, 13, 7, 4, 14, 2, 15, 16, 8, 1, 17, 18, 9, 19, 10, 5, 20, 21, 11, 6, 22, 3, 23, 24, 12, 25, 13, 7, 26, 4, 27, 28, 14, 2, 29, 30, 15, 31, 16, 8, 32, 1, 33, 34, 17, 35, 18, 9, 36, 37, 19

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

COMMENTS

As a fractal sequence, it contains infinitely many copies of itself: removing the first occurrence of each number leaves the original sequence.

REFERENCES

Clark Kimberling, "Fractal sequences and interspersions," Ars Combinatoria 45 (1997) 157-168.

LINKS

Clark Kimberling, Table of n, a(n) for n = 1..200

EXAMPLE

A northwest corner of the dispersion (A248513) of the "odious numbers" (A181155) follows:

1 ... 2 ... 3 ... 5 ... 9 ... 17 .... 33

4 ... 8 ... 15 .. 29 .. 57 .. 113 ... 225

6 ... 12 .. 23 .. 45 .. 89 .. 177 ... 353

7 ... 14 .. 27 .. 53 .. 105 .. 209 .. 417

10 .. 20 .. 39 .. 77 .. 153 .. 305 .. 609

The numbers 1, 2, 3, 4, 5 appear in rows 1, 1, 1, 2, 1, respectively, so that A248514 = (1, 1, 1, 2, 1, ...).

MATHEMATICA

r = 40; r1 = 10; (* r = # rows of T, r1 = # rows to show*);

c = 40; c1 = 12; (* c = # cols of T, c1 = # cols to show*);

x = GoldenRatio; s[n_] := s[n] = If[n < 1, 0, 2 n - Mod[Total[IntegerDigits[n - 1, 2]], 2]];

mex[list_] := NestWhile[#1 + 1 &, 1, Union[list][[#1]] <= #1 &, 1, Length[Union[list]]]; rows = {NestList[s, 1, c]};

Do[rows = Append[rows, NestList[s, mex[Flatten[rows]], r]], {r}];

t[i_, j_] := rows[[i, j]]; TableForm[Table[t[i, j], {i, 1, r1}, {j, 1, c1}]] (* A248513 array*)

u = Flatten[Table[t[k, n - k + 1], {n, 1, c1}, {k, 1, n}]] (* A248013 sequence*)

row[i_] := row[i] = Table[t[i, j], {j, 1, c}]

f[n_] := Select[Range[r], MemberQ[row[#], n] &]

v = Flatten[Table[f[n], {n, 1, 200}]] (* A248514 *)

CROSSREFS

Cf. A248513.

Sequence in context: A125158 A273823 A112384 * A123390 A306806 A306805

Adjacent sequences: A248511 A248512 A248513 * A248515 A248516 A248517

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 08 2014

STATUS

approved