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

1,2

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) 157-168.

Links

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

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

Cf. A003603, A019586, A035513.

Sequence in context: A183917 A181971 A104741 * A277813 A200154 A208825

Adjacent sequences: A167234 A167235 A167236 * A167238 A167239 A167240

Keyword

nonn

Author

Clark Kimberling, Oct 31 2009

Status

approved