Any irrational number will satisfy your request:
[tex]\pi, \sqrt{2}, \log_2(5)[/tex]
Step-by-step explanation:
[tex] \sqrt{2} \: \: \: and \: \: \: \\ \sqrt{3 } \: \: \: \: \: and \\ \pi[/tex]
are three numbers whose decimal expansions are non-terminating non-recurring.