

A167237


Lower trim of the Wythoff fractal sequence, A003603.


3



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

1,2


COMMENTS

A fractal sequence: if you delete the first occurrence of each positive
integer, the remaining sequence is the original. This procedure is called
upper trimming, in contrast to lower trimming, which consists of
subtracting 1 from each term of the original fractal sequence and then
deleting all 0's. In general, the lower trim of a fractal sequence is a
fractal sequence; in particular, the lower trim of A003603 is A167237.


REFERENCES

Clark Kimberling, "Fractal Sequences and Interspersions," Ars Combinatoria 45 (1997) 157168.


LINKS



FORMULA

Although A167237 is closely associated with the Wythoff array (A035513)
and Fibonacci numbers (A000045), it can be constructed independently.
First, construct the fractal sequence of the Wythoff array inductively
as described at A003603; then subtract 1 from all terms and delete
all 0's.


EXAMPLE

The first 7 rows in the construction of A003603 are
1
1
1 2
1 3 2
1 4 3 2 5
1 6 4 3 7 2 8 5
1 9 6 4 10 3 11 7 2 12 8 5 13
Subtracting 1 and deleting 0's leaves
1
2 1
3 2 1 4
5 4 2 6 1 7 4
8 5 3 9 2 10 6 1 11 7 4 12


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



