login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A132224 A dense normalized fractal sequence. 3
1, 1, 2, 1, 2, 3, 1, 4, 2, 3, 1, 4, 2, 3, 5, 1, 4, 2, 6, 3, 5, 1, 4, 7, 2, 6, 3, 5, 1, 8, 4, 7, 2, 6, 3, 5, 1, 8, 4, 7, 2, 6, 3, 5, 9, 1, 8, 4, 7, 2, 6, 3, 10, 5, 9, 1, 8, 4, 7, 2, 6, 11, 3, 10, 5, 9, 1, 8, 4, 7, 2, 12, 6, 11, 3, 10, 5, 9, 1, 8, 4, 7, 13, 2, 12, 6, 11, 3, 10, 5, 9, 1, 8, 4, 14, 7, 13, 2, 12, 6, 11, 3, 10, 5, 9, 1, 8, 15, 4, 14, 7, 13, 2, 12, 6, 11, 3, 10, 5, 9, 1, 16, 8, 15, 4, 14, 7, 13, 2, 12, 6, 11, 3, 10, 5, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
This sequence is also given by its placement sequence, A132226.
REFERENCES
C. Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.
LINKS
Clark Kimberling, Self-Containing Sequences, Selection Functions, and Parasequences, J. Int. Seq. Vol. 25 (2022), Article 22.2.1.
FORMULA
This is the normalization of A132223, formed by concatenating segments obtained from segments of A132223, as follows: segment 1 is 1. Segment 2 is 12. Segment 3 is 123, formed from the segment 1423 in A132223 by retaining only numbers up to 3. Segment 4 is 1423, formed from segment 1423 in A132223 by retaining only numbers up to 4. In general, the n-th segment of A132224 (this sequence) is a permutation of (1,2,3,...,n) formed from the first segment of A132223 that contains n by deleting from it all numbers greater than n.
EXAMPLE
The first 7 successive segments are 1, 12, 123, 1423, 14235, 142635.
1;
1, 2;
1, 2, 3;
1, 4, 2, 3;
1, 4, 2, 3, 5;
1, 4, 2, 6, 3, 5;
1, 4, 7, 2, 6, 3, 5;
1, 8, 4, 7, 2, 6, 3, 5;
1, 8, 4, 7, 2, 6, 3, 5, 9;
1, 8, 4, 7, 2, 6, 3, 10, 5, 9;
1, 8, 4, 7, 2, 6, 11, 3, 10, 5, 9;
1, 8, 4, 7, 2, 12, 6, 11, 3, 10, 5, 9;
1, 8, 4, 7, 13, 2, 12, 6, 11, 3, 10, 5, 9;
MAPLE
A132224_row := proc(n)
local r, a23r, a ;
for r from 1 do
a23r := [seq(A132223(r, k), k=1..2^r)] ;
if member(n, a23r) then
break;
end if;
end do:
a := [] ;
for i from 1 to nops(a23r) do
if op(i, a23r) <= n then
a := [op(a), op(i, a23r)] ;
end if;
end do:
a ;
end proc:
seq(op(A132224_row(n)), n=1..12) ; # R. J. Mathar, May 08 2016
MATHEMATICA
dense[n_] := FoldList[Riffle[#1, Range[2^#2, 2^(#2 - 1) + 1, -1]] &, {1, 2}, Range[2, n + 1]]; densefractal[n_] := Flatten[Table[Select[dense[n][[Position[dense[n], i, 2, 1][[1, 1]]]], # <= i &], {i, 2^n}]]; densefractal[5] (* Birkas Gyorgy, Apr 20 2011 *)
CROSSREFS
Cf. A132223.
Sequence in context: A358532 A143604 A021475 * A194961 A195110 A167198
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 14 2007
EXTENSIONS
Corrected and extended data by Vincenzo Librandi Dec 25 2019
STATUS
approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 05:39 EDT 2024. Contains 371235 sequences. (Running on oeis4.)