'Counting by ones' But, like Tom said, normally this would just be called counting unless you were explicitly contrasting it with something else, i.e. counting by tens, counting by hundreds.

I have never heard anybody say either one of those. You are simply "counting". In an unusual situation where you want to be extremely precise, you can say "I am counting with successive integers". You could also say "whole numbers" in place of "integers".

Neither. ‘By’ is correct. For example: To learn numbers in English you need to know how to count by ones to 20 then by 10s to 100. A common test of mental status is counting backwards from 100 by 7s.

"I am counting" means "normal counting" which is 1,2,3,4 etc. Usually we only specify if it is something different, so "I am counting in twos" or "by twos". I don't think "on" works here. I guess if you want to emphasize it you could say "I am counting in single digits." I hope that helps.