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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, 5, 10, 9, 1, 8, 4, 7, 2, 6, 11, 3, 5, 10, 9, 1, 8, 4, 7, 2, 12, 6, 11, 3, 5, 10, 9 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

This sequence is also given by its placement sequence, A132226.

Needs b-file.

REFERENCES

C. Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, preprint, 2007.

LINKS

Table of n, a(n) for n=1..78.

Clark Kimberling, Proper self-containing sequences, fractal sequences and para-sequences, unpublished manuscript, 2007, cached copy, with permission.

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: A264744 A143604 A021475 * A194961 A195110 A167198

Adjacent sequences:  A132221 A132222 A132223 * A132225 A132226 A132227

KEYWORD

nonn

AUTHOR

Clark Kimberling, Aug 14 2007

STATUS

approved

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Last modified October 18 16:14 EDT 2018. Contains 316323 sequences. (Running on oeis4.)