A167237 Lower trim of the Wythoff fractal sequence, A003603.

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

Offset: 1

Author

Clark Kimberling, Oct 31 2009

Keywords

• nonn

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.

Examples

			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
		

References

• Clark Kimberling, "Fractal Sequences and Interspersions," Ars Combinatoria 45 (1997) 157-168.

Crossrefs

Cf. A003603, A019586, A035513.

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.