For decades, mathematicians have been inching forward on a problem about which sets contain evenly spaced patterns of three numbers. Last month, two computer scientists blew past all of those results.
The thick orange line jumps along the first 15 terms of the smallest possible sequence of natural numbers that avoids any three-term arithmetic progressions.
- A lecturer at Stockholm University. Kelley and Meka, outsiders to the field of combinatorics, said they had found a new โ and dramatically lower โ limit on the size of a set of integers in which no three of them are evenly spaced (ruling out combinations like 3, 8 and 13 or 101, 201 and 301).
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