# 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[edit]

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

- 1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, 123, 148, 182, 204, 252, 290, 361, 401, 475, ... (sequence A005282 in the OEIS).

## Similar sequences[edit]

If we define , the resulting sequence is the same except each term is one less (that is, 0, 1, 3, 7, 12, 20, 30, 44, 65, 80, 96, ... OEIS: A025582).

## History[edit]

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

## References[edit]

- S. R. Finch,
*Mathematical Constants*, Cambridge (2003): Section 2.20.2 - R. K. Guy
*Unsolved Problems in Number Theory*, New York: Springer (2003)