For some interval I ⊂ ⊂ R , suppose that f : I → → I is a continuous function. The number x is called a periodic point of period m if f ( m ) ( x ) = x , where f ( m ) denotes the iterated function obtained by composition of m copies of f . The number x is said to have least period m if, in addition, f ( k ) ( x ) ≠ ≠ x for all 0 < k < m . Sharkovskii's theorem concerns the possible least periods of periodic points of f . Consider the following ordering of the positive integers, sometimes called the Sharkovskii ordering: 3 5 7 9 11 … … ( 2 n + 1 ) ⋅ ⋅ 2 0 … … 3 ⋅ ⋅ 2 5 ⋅ ⋅ 2 7 ⋅ ⋅ 2 9 ⋅ ⋅ 2 11 ⋅ ⋅ 2 … … ( 2 n + 1 ) ⋅ ⋅ 2 1 … … 3 ⋅ ⋅ 2 2 5 ⋅ ⋅ 2 2 7 ⋅ ⋅ 2 2 9 ⋅ ⋅ 2 2 11 ⋅ ⋅ 2 2 … … ( 2 n + 1 ) ⋅ ⋅ 2 2 … … 3 ⋅ ⋅ 2 3 5 ⋅ ⋅ 2 3 7 ⋅ ⋅ 2 3 9 ⋅ ⋅ 2 3 11 ⋅ ⋅ 2 3 … … ( 2 n + 1 ) ⋅ ⋅ 2 3 … … ⋮ ⋮ … … 2 n … … 2 4 2 3 2 2 2 1