A167404 Complete lower trim array of the Wythoff fractal sequence, A003603.

1, 1, 1, 1, 2, 1, 2, 1, 2, 1, 1, 3, 1, 2, 1, 3, 2, 3, 3, 2, 1, 2, 1, 4, 1, 3, 2, 1, 1, 4, 2, 4, 4, 3, 2, 1, 4, 5, 1, 5, 1, 4, 3, 2, 1, 3, 3, 5, 2, 5, 1, 4, 3, 2, 1, 2, 2, 6, 6, 2, 5, 5, 4, 3, 2, 1, 5, 6, 3, 3, 6, 6, 1, 5, 4, 3, 2, 1, 1, 1, 7, 1, 7, 2, 6, 1, 5, 4, 3, 2, 1, 6, 7, 4, 7, 3, 7, 2, 6, 6, 5, 4, 3, 2, 1

Offset

1,5

Comments

The lower trim sequence of a fractal sequence s is the fractal sequence

remaining after all 0's are deleted from the sequence s-1. Row n of A167404

consists of successive lower trim sequences beginning with A003603. Thus

every row is a fractal sequence. It is easy to prove that the combinatorial

limit or these rows is the sequence (1,2,3,4,5,6,...) = A000027.

References

Clark Kimberling, "Fractal sequences and interspersions," Ars Combinatoria 45 (1997) 157-168.

Links

Table of n, a(n) for n=1..105.

Example

First five rows:
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 ... = 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 .... = A167237
1 2 1 3 4 2 1 5 6 3 7 4 2 8 1 9 5 10 6 3 11 12 7 4 13 ...
1 2 3 1 4 5 2 6 3 1 7 8 4 9 5 2 10 11 6 3 12 1 13 7 14 ...
1 2 3 4 1 5 2 6 7 3 8 4 1 9 10 5 2 11 12 6 13 7 3 14 15 ...

Crossrefs

Cf. A003603, A167237, A035513.

Sequence in context: A249973 A343854 A069349 * A280223 A062754 A342846

Adjacent sequences: A167401 A167402 A167403 * A167405 A167406 A167407

Keyword

nonn,tabl

Author

Clark Kimberling, Nov 02 2009

Status

approved