Is a concatenation of random numbers better than a single random number?

So is the concatenated random number better than a single random number?

If the random generator really produces random data then it will not matter.

... it would be harder to predict the next number in case there was an issue with the random number generator.

If the issue is that the random generator is not that random at all then it might even be better for an attacker to get as much last outputs as possible because then the behavior could be better to predict. Of course this assumption depends highly on the internals of the random generator, so no general answer is possible.

But in general: if you need really good random data you should use a proper random generator. Your method will not improve the quality of the output if the random generator is bad, i.e it stays predictable. If you actually don't need true random data but only want to make sure that you get somewhat random data without a bias you should be careful because depending on how exactly you do it your method might add a bias to the output.