Mian-Chowla sequence
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In mathematics, the Mian-Chowla sequence is an integer sequence defined recursively in the following way. Let
- a1 = 1.
Then for n > 1, an is the smallest integer such that the pairwise sum
- ai + aj
is distinct, for all i and j less then or equal to n.
Initially, with a1, there is only one pairwise sum, 1+1=2. The next term in the sequence, a2, is 2 since the pairwise sums then are 2, 3 and 4, i.e., they are distinct. Then, a3 can't be 3 because there would be the non-distinct pairwise sums 1 + 3 = 2 + 2 = 4. We find then that a3 = 4, with the pairwise sums being 2, 3, 4, 5, 6 and 8. The sequence continues 8, 13, 21, 31, 45, 66, 81, 97, 123, 148, 182, 204, 252, 290, 361, 401, 475, ... (sequence A005282 in OEIS).
If we define a1 = 0, the resulting sequence is the same except each term is one less.
Rachel Lewis noticed that
,
a constant listed in Finch's book.
[edit] References
- S. R. Finch, Mathematical Constants, Cambridge (2003): Section 2.20.2
- R. K. Guy Unsolved Problems in Number Theory, New York: Springer (2003)
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