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Erdős Problem #265 — Let 1≤a1<a2<⋯1\leq a_1<a_2<\cdots be an increasing sequence of integers. How fast can an→∞a_n\to \infty grow if ∑1anand∑1an−1\sum\frac{1}{a_n}\quad\textrm{and}\quad\sum\frac{1}{a_n-1} are both rational?

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Let 1≤a1<a2<⋯1\leq a_1<a_2<\cdots be an increasing sequence of integers. How fast can an→∞a_n\to \infty grow if ∑1anand∑1an−1\sum\frac{1}{a_n}\quad\textrm{and}\quad\sum\frac{1}{a_n-1} are both rational?

References

Primary source

ULAM AI, UnsolvedMath dataset, Erdős Problems set, revision b9437975f3c873f635a13c48f8b022f5ba80898a; CC BY 4.0.

Additional references

UnsolvedMath, Erdős Problems set, ULAM AI, licensed CC BY 4.0.

irrationality
InErdős Problems
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