If you want to print an integer to stdout, you need to convert it to a string first, since that's all stdout understands. If you want to print two integers to stdout, you need to convert both of them to a string first. If you want to print three integers to stdout, you need to convert all three of them to a string first. If you want to print one billion integers to stdout, you need to convert all one billion of them to a string first.
There's nothing you, we, or Ruby, or really any programming language can do about that.
You could try interleaving the conversion with the I/O by doing a lazy stream implementation. You could try to do the conversion and the I/O in parallel, by doing a lazy stream implementation and separating the conversion and the I/O into two separate threads. (Be sure to use a Ruby implementation which can actually execute parallel threads, not all of them can: MRI, YARV and Rubinius can't, for example.)
You can parallelize the conversion, by converting separate chunks in the array in separate threads in parallel. You can even buy a billion core machine and convert all billion integers at the same time in parallel.
But even then, the fact of the matter remains: every single integer needs to be converted. Whether you do that one after the other first, and then print them or do it one after the other interleaved with the I/O or do it one after the other in parallel with the I/O or even convert all of them at the same time on a billion core CPU: the number of needed conversions does not magically decrease. A large number of integers means a large number of conversions. Even if you do all billion conversions in a billion core CPU in parallel, it's still a billion conversions, i.e. a billion calls to to_s
.