Geodesic
Binary BBP-formulae for logarithms and generalized Gaussian-Mersenne primes
Journal of integer sequences, Tome 6 (2003) no. 3
Constants of the form

$ C = \sum_{k=0}^\infty \frac{p(k)}{q(k)b^k} $

where $p$ and $q$ are integer polynomials, $\deg p \deg q$, and $p(k)/q(k)$ is non-singular for non-negative $k$ and $b\geq 2$, have special properties. The $n$th digit (base $b$) of $C$ may be calculated in (essentially) linear time without computing its preceding digits, and constants of this form are conjectured to be either rational or normal to base $b$. This paper constructs such formulae for constants of the form $\log p$ for many primes $p$. This holds for all Gaussian-Mersenne primes and for a larger class of "generalized Gaussian-Mersenne primes". Finally, connections to Aurifeuillian factorizations are made.
Classification : 11Y05, 11A41, 11B99, 11T22, 11Y60
Keywords: primes, Gaussian-mersenne, BBP, aurifeuillian 
@article{JIS_2003__6_3_a3,
     author = {Chamberland,  Marc},
     title = {Binary {BBP-formulae} for logarithms and generalized {Gaussian-Mersenne} primes},
     journal = {Journal of integer sequences},
     year = {2003},
     volume = {6},
     number = {3},
     zbl = {1073.11076},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_3_a3/}
}
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Chamberland,  Marc. Binary BBP-formulae for logarithms and generalized Gaussian-Mersenne primes. Journal of integer sequences, Tome 6 (2003) no. 3. http://geodesic.mathdoc.fr/item/JIS_2003__6_3_a3/