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

Author

Clark Kimberling, Nov 02 2009

Keywords

• nonn
• tabl

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.

Examples

			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 ...
		

References

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

Crossrefs

Cf. A003603, A167237, A035513.