Stanley sequence

<p>In mathematics, a Stanley sequence is an <a href="/facts/Integer_sequence/4l3pev7C">integer sequence</a> generated by a <a href="/facts/Greedy_algorithm/alfsekco">greedy algorithm</a> that chooses the sequence members to avoid <a href="/facts/Arithmetic_progression/c4ew9Xoq">arithmetic progressions</a>. If 
  
    
      
        S
      
    
    {\displaystyle S}
  
 is a finite set of non-negative integers on which no three elements form an arithmetic progression (that is, a <a href="/facts/Salem%E2%80%93Spencer_set/aWogz0JA">Salem–Spencer set</a>), then the Stanley sequence generated from 
  
    
      
        S
      
    
    {\displaystyle S}
  
 starts from the elements of 
  
    
      
        S
      
    
    {\displaystyle S}
  
, in sorted order, and then repeatedly chooses each successive element of the sequence to be a number that is larger than the already-chosen numbers and does not form any three-term arithmetic progression with them.
These sequences are named after <a href="/facts/Richard_P._Stanley/8bQ4QrLM">Richard P. Stanley</a>.
</p>

Stanley sequence open-in-new

Stanley sequence