Correct, OP's example contained an O(n) function: > For example, the following function is O(n) because the algorithm grows in proportion to its input n: [...]

Correct, OP's example contained an O(n) function: > For example, the following function is O(n) because the algorithm grows in proportion to its input n: [...] OP's question was whether there exists a similarly simple example of O(log n), which is not related to what anonymouz was commenting on. (or I'm misunderstanding?)