Sets of integers with nonlong arithmetic progressions generated by the greedy algorithm
Authors: Joseph L. Gerver and L. Thomas Ramsey
Journal: Math. Comp. 33 (1979), 1353-1359
MSC: Primary 10L10
MathSciNet review: 537982
Abstract: Let be the set of positive integers containing no arithmetic progression of k terms, generated by the greedy algorithm. A heuristic formula, supported by computational evidence, is derived for the asymptotic density of in the case where k is composite. This formula, with a couple of additional assumptions, is shown to imply that the greedy algorithm would not maximize over all S with no arithmetic progression of k terms. Finally it is proved, without relying on any conjecture, that for all , the number of elements of which are less than n is greater than for sufficiently large n.
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