The primes nearest to the nonnegative integers n = 0, 1, 2, ..., assigning ties to the smaller prime, are 2, 2, 2, 3, 3, 5, 5, 7, 7, 7, 11, 11, 11, 13, ... (OEIS A051697). If ties are instead assigned to the larger prime, the corresponding sequence is instead 2, 2, 2, 3, 5, 5, 7, 7, 7, 11, 11, 11, 13, 13, ... (OEIS A077018), which is identical except that one of the 3s is omitted.

prime distance | prime gaps