Mian–Chowla sequence

From Wikipedia, the free encyclopedia
Jump to: navigation, search

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 the 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, ... OEISA025582).

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)