1. The problem statement, all variables and given/known data An integer sequence has cropped up in research I'm doing, but I'm having trouble understanding it. A number n is on this integer sequence if there is no m>0 such that n+m is divisible by 6m-1, 6m+1, 8m-1 or 8m+1. http://oeis.org/A109598 What I'm wondering is if there is some quick and easy way to ascertain whether a given number belongs on this list or not. It seems like each number would require a mini proof. For example, 5 is on the list. How do we know that there is *no m at all* such that 5+m is divisible by 6m-1, 6m+1, 8m-1 or 8m+1? How do we exhaust all possibilities for m? It seems like there is a method here that I am missing. 2. Relevant equations n+m=6m-1 n+m=6m+1 n+m=8m-1 n+m=8m+1 3. The attempt at a solution I tried to write to the author of this sequence, David Wasserman, and have not heard back from him. It is possible the e-mail address I used is out of date, as his web site is also quite out of date.