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Date: 17-3-2020
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Date: 25-2-2020
665
Date: 24-1-2020
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The sequence produced by starting with and applying the greedy algorithm in the following way: for each , let be the least integer exceeding for which are all distinct, with .
This procedure generates the sequence 1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, 123, 148, 182, 204, 252, 290, ... (OEIS A005282). The reciprocal sum of the sequence,
satisfies
(R. Lewis).
REFERENCES:
Mian, A. M. and Chowla, S. D. "On the -Sequences of Sidon." Proc. Nat. Acad. Sci. India A14, 3-4, 1944.
Guy, R. K. "-Sequences." §E28 in Unsolved Problems in Number Theory, 2nd ed. New York: Springer-Verlag, pp. 228-229, 1994.
Sloane, N. J. A. Sequence A005282/M1094 in "The On-Line Encyclopedia of Integer Sequences."
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