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A sequence defined from a Finite sequence 
, 
, ..., 
 by defining 
,
where 
 is the Mex (minimum excluded value).
See also Max Sequence, Mex
References
Guy, R. K.  ``Max and Mex Sequences.''  §E27 in Unsolved Problems in Number Theory, 2nd ed.
  New York: Springer-Verlag, pp. 227-228, 1994.