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,
Mian, A. M. and Chowla, S. D. "On the -Sequences of Sidon." Proc.
Nat. Acad. Sci. IndiaA14, 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."