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Erdős Problem #260 — Let a1<a2<⋯a_1<a_2<\cdots be an increasing sequence such that an/n→∞a_n/n\to \infty. Is the sum ∑nan2an\sum_n \frac{a_n}{2^{a_n}} irrational?

About 52 years old · traced to

Let a1<a2<⋯a_1<a_2<\cdots be an increasing sequence such that an/n→∞a_n/n\to \infty. Is the sum ∑nan2an\sum_n \frac{a_n}{2^{a_n}} irrational?

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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