Mian-Chowla Sequence

The sequence produced by starting with $a_1=1$ and applying the Greedy Algorithm in the following way: for each $k\geq 2$, let $a_k$ be the least Integer exceeding $a_{k-1}$ for which $a_j+a_k$ are all distinct, with $1\leq j\leq k$. This procedure generates the sequence 1, 2, 4, 8, 13, 21, 31, 45, 66, 81, 97, 123, 148, 182, 204, 252, 290, ... (Sloane's A005282). The Reciprocal sum of the sequence,

$$S\equiv \sum_{i=1}^\infty {1\over a_i},$$

satisfies

$$2.1568\leq S\leq 2.1596.$$

See also A-Sequence, B2-Sequence

References

Guy, R. K. ``$B_2$-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 ``An On-Line Version of the Encyclopedia of Integer Sequences.'' http://www.research.att.com/~njas/sequences/eisonline.html and Sloane, N. J. A. and Plouffe, S. The Encyclopedia of Integer Sequences. San Diego: Academic Press, 1995.