Some Curious Sequences Constructed with the Greedyalgorithma

@inproceedings{Hill1978SomeCS,
  title={Some Curious Sequences Constructed with the Greedyalgorithma},
  author={. M. OdlyzkoBell LaboratoriesMurray Hill and New JerseyR. P. StanleyMassachusetts},
  year={1978}
}
  • . M. OdlyzkoBell LaboratoriesMurray Hill, New JerseyR. P. StanleyMassachusetts
  • Published 1978
Given a xed positive integer k, deene a sequence S(k) of positive integers 0 = a 0 < a 1 < : : : by the conditions: (i) a 1 = k (ii) having chosen a 0 , a 1 ; : : : ; a n (n 1), let a n+1 be the least integer such that a n+1 > a n and such that the sequence a 1 , a 1 ; : : : ; a n ; a n+1 contains no three terms (not necessarily consecutive) in an arithmetic progression. One might hope that the sequence S(k) (for a suitable value of k) has the least rate of growth among all sequences 0 = b 0… CONTINUE READING

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