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Binary BBP-Formulae for Logarithms
and Generalized Gaussian-Mersenne Primes
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Marc Chamberland

Department of Mathematics and Computer Science

Grinnell College

Grinnell, IA 50112

USA

**Abstract:**

Constants of the form

where *p* and *q* are integer polynomials,
,
and *p*(*k*)/*q*(*k*) is
non-singular for non-negative *k* and ,
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 for many primes *p*. This holds for all Gaussian-Mersenne primes and
for a larger class of ``generalized Guassian-Mersenne primes''.
Finally, connections to Aurifeuillian factorizations are made.

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(Concerned with sequence
A057429
.)

Received July 15, 2003;
revised version received October 24, 2003.
Published in *Journal of Integer Sequences*
October 25, 2003.

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