User blog comment:Denis Maksudov/Slowly growing ordinal function and FS up to BHO./@comment-28606698-20170402064919/@comment-1605058-20170402121801

It's important to keep in mind though that this pattern fails for some larger ordinals - for example, \(\Omega_\omega\) has cofinality \(\omega\) (it's a limit of \(\Omega_1,\Omega_2,\dots\)), but then \(\Omega_{\omega+1}\) is its own cofinality.