A few years ago Don Blazys caused a ripple of excitation among numerologists by presenting a real number which, applying an iterative computation recipe, produced all prime numbers. The procedure is one of an infinity of possible mappings between subsets of real numbers and subsets of integer sequences. In this particular case, the source set is that of irrational real numbers greater than 1, and its image is the set of sequences of non-decreasing natural numbers. It turns out, however, that the mapping, denoted here as bx(x), is a bijection between the two sets, thus enabling the existence of an inverse mapping bf(s) which, in addition, can be cast as a special type of generalized continued fractions. This article presents the definitions, the proofs of the bijection and the pertinent algorithms. It also analyses some simple properties of these mappings.
View/download the open-access full-text PDF version
Please, cite this online document as:
Sykora S., Blazys Expansions and Continued Fractions,
Stan's Library, Vol.IV, December 2013, DOI: 10.3247/SL4Math13.001 .
Your comments are welcome and will appear here