login
This site is supported by donations to The OEIS Foundation.

 

Logo

"Email this user" was broken Aug 14 to 9am Aug 16. If you sent someone a message in this period, please send it again.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A248514 Fractal sequence of the dispersion of the "odious numbers". 2
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 occurence 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 A162598 A088208

Adjacent sequences:  A248511 A248512 A248513 * A248515 A248516 A248517

KEYWORD

nonn,easy

AUTHOR

Clark Kimberling, Oct 08 2014

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified August 17 06:13 EDT 2017. Contains 290635 sequences.