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Mian-Chowla Sequence

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The sequence produced by starting with a_1=1 and applying the greedy algorithm in the following way: for each k>=2, let a_k be the least integer exceeding a_(k-1) for which a_i+a_j are all distinct, with 1<=i<=j<=k.

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,

S=sum_(i=1)^infty1/(a_i),

satisfies

2.158435<=S<=2.158677

(R. Lewis).

See also

A-Sequence, B2-Sequence

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References

Mian, A. M. and Chowla, S. D. "On the B_2-Sequences of Sidon." Proc. Nat. Acad. Sci. India A14, 3-4, 1944.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 "The On-Line Encyclopedia of Integer Sequences."

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Mian-Chowla Sequence

Cite this as:

Weisstein, Eric W. "Mian-Chowla Sequence." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Mian-ChowlaSequence.html

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