Mian–Chowla sequence


In mathematics, the Mian–Chowla sequence is an integer sequence defined
recursively in the following way. The sequence starts with
Then for, is the smallest integer such that every pairwise sum
is distinct, for all and less than or equal to.

Properties

Initially, with, there is only one pairwise sum, 1 + 1 = 2. The next term in the sequence,, is 2 since the pairwise sums then are 2, 3 and 4, i.e., they are distinct. Then, can't be 3 because there would be the non-distinct pairwise sums 1 + 3 = 2 + 2 = 4. We find then that, with the pairwise sums being 2, 3, 4, 5, 6 and 8. The sequence thus begins

Similar sequences

If we define, the resulting sequence is the same except each term is one less.

History

The sequence was invented by Abdul Majid Mian and Sarvadaman Chowla.