Highly Influenced

# 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} }

- 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