Formula doesn't work until I populate each field in the formula at least one time, then works for the one record. Needs to be repeated in each record?

I have a strange situation. I have 3 phone fields, Phone, Phone 2, Phone 3. I have a formula to then display the phone number somewhere else in the record (in the same table).

I want to display the most recent Phone number. If Phone 3 has no number display Phone 2, if Phone 2 has no number display Phone.

if 'Phone 3' != 0 then
'Phone 3'
else
if 'Phone 2' != 0 then 'Phone 2' else Phone end
end

The Formula works BUT only if I populate Phone, Phone 2, and Phone 3 at least one time. If a record has only one Phone, the formula field to display the number doesn't display the number from Phone until I populate Phone 2 and Phone 3 at least one time Once I do this it then works for the one record. 

If I open another client record, the phone doesn't display in the formula field until I populate Phone, Phone 2, and Phone 3 at least 1x for that individual record.

Any help is appreciated. 

Thanks, Pat