On -free sequences of integers

Author:
Samuel S. Wagstaff

Journal:
Math. Comp. **26** (1972), 767-771

MSC:
Primary 10-04; Secondary 10L99

DOI:
https://doi.org/10.1090/S0025-5718-1972-0325500-5

MathSciNet review:
0325500

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Abstract: Let denote the cardinality of the largest subsequence of , which contains no numbers in arithmetical progression. (Such a sequence is called -free.) is computed (on an IBM 360/65) for , and various values of to about 50. The results support the old conjecture that for all , the limit . The results , and are obtained. Several cases of a (disproved) conjecture of G. Szekeres are verified, including .

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1972-0325500-5

Keywords:
-free sequences,
arithmetic progressions in sequences

Article copyright:
© Copyright 1972
American Mathematical Society