Call a_1<a_2<… an irrationality sequence if ∑_n≥11/(t_na_n) is irrational for every integer sequence t_n≥1. How slowly can an irrationality sequence grow?

Erdős Problem #262 — Slowly growing irrationality sequences

About 46 years old · traced to 1980

Call $a_1<a_2<\cdots$ an irrationality sequence if $\sum_{n\geq1}1/(t_na_n)$ is irrational for every integer sequence $t_n\geq1$ . How slowly can an irrationality sequence grow?

References

Primary source

P. Erdős and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L'Enseignement Mathématique 28 (1980).

Additional references

P. Erdős and R. L. Graham, Old and new problems and results in combinatorial number theory, Monographies de L'Enseignement Mathématique 28 (1980).

irrationality

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