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
Vincenzo Librandi, Table of n, a(n) for n = 1..8256
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
KEYWORD
nonn
AUTHOR
Clark Kimberling, Aug 14 2007
EXTENSIONS
Corrected and extended data by Vincenzo Librandi Dec 25 2019
STATUS
approved