time complexity – How to find infinite set X, which satisfies T(n)=Ω(n) when n∈X

Consider the following recurrence relationship.

begin{eqnarray}
T(n) &=&
begin{cases}
Tleft(displaystylefrac{n}{2}right) + 1, &n mbox{is even number}& \
2Tleft(displaystylefrac{n-1}{2}right), &n mbox{is odd number}&
end{cases} nonumber \
T(1) &=& 1
end{eqnarray}

How to find infinite set X, which satisfies T(n)=Ω(n) when n∈X ?
I want to know the example of X and the process how to get it.