A167404 - OEIS

%I #4 Apr 07 2020 22:42:28

%S 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,

%T 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,

%U 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

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

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

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

%C consists of successive lower trim sequences beginning with A003603. Thus

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

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

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

%e First five rows:

%e 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

%e 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

%e 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 ...

%e 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 ...

%e 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 ...

%Y Cf. A003603, A167237, A035513.

%K nonn,tabl

%O 1,5

%A _Clark Kimberling_, Nov 02 2009