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 .
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Transcription
Contents
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 nondistinct 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
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
The sequence was invented by Abdul Majid Mian and Sarvadaman Chowla.
References
 S. R. Finch, Mathematical Constants, Cambridge (2003): Section 2.20.2
 R. K. Guy Unsolved Problems in Number Theory, New York: Springer (2003)