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A167404 Complete lower trim array of the Wythoff fractal sequence, A003603. 1
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 (list; table; graph; refs; listen; history; text; internal format)
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
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
Sequence in context: A249973 A343854 A069349 * A280223 A062754 A342846
KEYWORD
nonn,tabl
AUTHOR
Clark Kimberling, Nov 02 2009
STATUS
approved

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Last modified July 13 14:24 EDT 2024. Contains 374284 sequences. (Running on oeis4.)