number-theory / Digital number theory

Binary Digits of the Erdős-Borwein Constant

Does the block $11$ occur infinitely often in the base-$2$ expansion of the Erdős-Borwein constant $E = \sum_{n \ge 1} \frac{1}{2^n - 1}$? Posed by Crandall in 2012.

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number-theoryMay 22, 2026Significance 10/100Registry: unreviewed

Binary Digits of the Erdős-Borwein Constant

Prior state unknownproved

Does the block $11$ occur infinitely often in the base-$2$ expansion of the Erdős-Borwein constant $E = \sum_{n \ge 1} \frac{1}{2^n - 1}$? Posed by Crandall in 2012.

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Does the block $11$ occur infinitely often in the base-$2$ expansion of the Erdős-Borwein constant $E = \sum_{n \ge 1} \frac{1}{2^n - 1}$? Posed by Crandall in 2012.

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