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A167237 Lower trim of the Wythoff fractal sequence, A003603.

%I A167237 #7 Apr 06 2020 20:37:37
%S A167237 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,
%T A167237 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,
%U A167237 25,2,26,16,10,27,6,28,17,1,29,18,11,30,7,31,19,4,32,20,12
%N A167237 Lower trim of the Wythoff fractal sequence, A003603.
%C A167237 A fractal sequence: if you delete the first occurrence of each positive
%C A167237 integer, the remaining sequence is the original. This procedure is called
%C A167237 upper trimming, in contrast to lower trimming, which consists of
%C A167237 subtracting 1 from each term of the original fractal sequence and then
%C A167237 deleting all 0's. In general, the lower trim of a fractal sequence is a
%C A167237 fractal sequence; in particular, the lower trim of A003603 is A167237.
%D A167237 Clark Kimberling, "Fractal Sequences and Interspersions," Ars Combinatoria 45 (1997) 157-168.
%F A167237 Although A167237 is closely associated with the Wythoff array (A035513)
%F A167237 and Fibonacci numbers (A000045), it can be constructed independently.
%F A167237 First, construct the fractal sequence of the Wythoff array inductively
%F A167237 as described at A003603; then subtract 1 from all terms and delete
%F A167237 all 0's.
%e A167237 The first 7 rows in the construction of A003603 are
%e A167237 1
%e A167237 1
%e A167237 1 2
%e A167237 1 3 2
%e A167237 1 4 3 2 5
%e A167237 1 6 4 3 7 2 8 5
%e A167237 1 9 6 4 10 3 11 7 2 12 8 5 13
%e A167237 Subtracting 1 and deleting 0's leaves
%e A167237 1
%e A167237 2 1
%e A167237 3 2 1 4
%e A167237 5 4 2 6 1 7 4
%e A167237 8 5 3 9 2 10 6 1 11 7 4 12
%Y A167237 Cf. A003603, A019586, A035513.
%K A167237 nonn
%O A167237 1,2
%A A167237 _Clark Kimberling_, Oct 31 2009