For Exercises 52–62, refer to the following. Call a sequence musical if repeatedly applying deflation to it eventually results in a single .
58. Exercises 53–56 give necessary conditions for a sequence to be musical. Are those conditions sufficient? That is, if a sequence does not contain or , and it does not end in or , must it be a musical sequence? (This is the kind of question that mathematicians ask in an effort to pin down the characteristics of a musical sequence.)