Volume 12 (2012)
Volume 11 (2011)
Volume 10 (2010)
Most Downloaded Articles
- Artin's Primitive Root Conjecture – A Survey by Moree, Pieter
- On the Number of Carries Occurring in an Addition Mod by Flori, Jean-Pierre and Randriam, Hugues
- A -Expansion Associated to Sturmian Sequences by Nakano, Fumihiko and Sadahiro, Taizo
- An Explicit Bound for Aliquot Cycles of Repdigits by Broughan, Kevin A.
The Googol-th Bit of the Erdős–Borwein Constant
1Center for Advanced Computation, Reed College, Portland, Oregon, USA
Citation Information: . Volume 12, Issue 5, Pages 811–840, ISSN (Online) 1867-0652, ISSN (Print) 1867-0652, DOI: 10.1515/integers-2012-0007, October 2012
- Published Online:
The Erdős–Borwein constant is a sum over all Mersenne reciprocals, namely
Although E is known to be irrational, the nature of the asymptotic distribution of its binary strings remains mysterious. Herein, we invoke nontrivial properties of the classical divisor function to establish that the googol-th bit, i.e., the bit in position to the right of the point is a `1.' Equivalently, the integer
is odd. Methods are also indicated for resolving contiguously the first bits (one full Terabyte) in about one day on modest machinery.