

A167198


Fractal sequence of the interspersion A083047.


3



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

1,3


COMMENTS

As a fractal sequence, if the first occurrence of each term is deleted, the remaining sequence is the original. In general, the interspersion of a fractal sequence is constructed by rows: row r consists of all n, such that a(n)=r; in particular, A083047 is constructed in this way from A167198.
a(n1) gives the row number which contains n in the dual Wythoff array A126714 (beginning the row count at 1), see also A223025 and A019586.  Casey Mongoven, Mar 11 2013


REFERENCES

Clark Kimberling, Stolarsky interspersions, Ars Combinatoria 39 (1995), 129138.


LINKS

Table of n, a(n) for n=1..85.
Clark Kimberling, The first column of an interspersion, The Fibonacci Quarterly 32 (1994), 301315.


FORMULA

Following is a construction that avoids reference to A083047.
Write initial rows:
Row 1: .... 1
Row 2: .... 1
Row 3: .... 2..1
Row 4: .... 2..3..1
For n>=4, to form row n+1, let k be the least positive integer not yet used; write row n, and right before the first number that is also in row n1, place k; right before the next number that is also in row n1, place k+1, and continue. A167198 is the concatenation of the rows. (If "before" is replaced by "after", the resulting fractal sequence is A003603, and the associated interspersion is the Wythoff array, A035513.)


EXAMPLE

To produce row 5, first write row 4: 2,3,1, then place 4 right before 2, and then place 5 right before 1, getting 4,2,3,5,1.


CROSSREFS

Cf. A003603, A083047, A035513, A000045.
Sequence in context: A132224 A194961 A195110 * A295540 A133299 A286537
Adjacent sequences: A167195 A167196 A167197 * A167199 A167200 A167201


KEYWORD

nonn


AUTHOR

Clark Kimberling, Oct 30 2009


STATUS

approved



