A number of results on prime numbers take the form “a random sequence with some growth restriction would have the following statistics; the primes, despite not being random, likewise have those statistics”. (A basic one being Dirichlet’s theorem.) Consequently, any tiny variation on the primes will looks like a random sequence and therefore give a really annoying math puzzle. I love love love having the OEIS around, but am not a big fan of these puzzles.
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