Is there a way to verify if numeric data was falsified? Would a simple randomness test work in this situation? I have a string of numbers that are intended to represent certain stats over time, but some of the numbers appear to be staged to my eye, including a lot of repeating integers (e.g. 121, 5335, etc.) and other signs that the data is not natural. The numbers follow a trend as expected, so they are not completely random, but is there a statistical test in R that I could use to give more insight into whether the data was falsified?

There are some common statistical techniques used in fraud detection that may be applicable.  A common test is to look at the distribution of first-digits in the number and compare this to Benford's law using appropriate statistical tests.    If you are interested in repeated digits or other similar phenomena you can use various kinds of runs-tests on the lower-order digits.  In all such cases you should be careful to check that the statistical assumptions underlying the tests are reasonable in the particular context where your data has arisen.  People sometimes overdiagnose fraudulent data by failing to consider deviations from assumptions that might legitimately occur in some contexts.
