Let 1≤ a_1<a_2<… be a sequence of integers such that limsup fraca_nn=∞. Is ∑_n=1^∞ frac12^a_n transcendental?

Erdős Problem #247 — Let $1\leq a_1<a_2<\cdots$ be a sequence of integers such that $\limsup \frac{a_n}{n}=\infty.$ Is $\sum_{n=1}^\infty \frac{1}{2^{a_n}}$ transcendental?

About 51 years old · traced to 1975

Let $1\leq a_1<a_2<\cdots$ be a sequence of integers such that $\limsup \frac{a_n}{n}=\infty.$ Is $\sum_{n=1}^\infty \frac{1}{2^{a_n}}$ transcendental?

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 number-theory

InErdős Problems

Posted 1 month ago · edited 3 weeks ago

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