A386439 - OEIS

A386439

Decimal expansion of the maximal density of a set of positive integers free of subsets of the form {n, 2n, 3n}.

8, 0, 0, 9, 6, 5, 7, 5, 5, 0, 0, 6, 5, 5, 8, 9, 8, 9, 0, 9, 0, 4, 2, 0, 3, 2, 6, 3, 8, 8, 0, 8, 2, 4, 1

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OFFSET

0,1

COMMENTS

Graham, Spencer, and Witsenhausen (1977) showed that the density is equal to (1/3) Sum_{k in K} 1 / d_k, where d_1 < d_2 < ... are the 3-smooth numbers (A003586) and K is the sequence A004059. It is an open question whether the number is irrational.

LINKS

Table of n, a(n) for n=0..34.

Thomas Bloom, Erdős Problem #168.

Sean Eberhard, SageMath script for computing the constant from A004059

R. L. Graham, H. S. Witsenhausen, and J. H. Spencer, On extremal density theorems for linear forms, Number theory and algebra, pp. 103-109, Academic Press, New York-London, 1977.

EXAMPLE

0.80096575500655898909042032638808241...

CROSSREFS

Cf. A003586, A004059, A057561, A094708.

Sequence in context: A114611 A219241 A257397 * A075448 A271407 A347801

Adjacent sequences: A386436 A386437 A386438 * A386440 A386441 A386442

KEYWORD

nonn,cons,more

AUTHOR

Sean Eberhard, Sep 18 2025

STATUS

approved