On free sequences of integers
Author:
Samuel S. Wagstaff
Journal:
Math. Comp. 26 (1972), 767771
MSC:
Primary 1004; Secondary 10L99
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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 S. S. Wagstaff, ``On sequences of integers with no 4, or no 5 numbers in arithmetical progression,'' Math. Comp., v. 21, 1967, pp. 695699. MR 36 #5061. MR 0222009 (36:5061)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718197203255005
PII:
S 00255718(1972)03255005
Keywords:
free sequences,
arithmetic progressions in sequences
Article copyright:
© Copyright 1972
American Mathematical Society
