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The upper-trimmed subsequence of 
 is the sequence 
 obtained by dropping the first occurrence of
 for each 
.  If 
 is a Fractal Sequence, then 
.
See also Lower-Trimmed Subsequence
References
Kimberling, C.  ``Fractal Sequences and Interspersions.''  Ars Combin. 45, 157-168, 1997.