Additive irreducibles in \alpha-expansions
Peter J. Grabner, Helmut Prodinger · Publicationes Mathematicae Debrecen · 2012
The Bergman number system uses the base α = 1+ √ 5 2 , the digits 0 and 1, and the condition that adjacent ones are forbidden.We are interested in those positive integers such that replacing one or more of the ones never results again in a positive integer; they are called (additively) irreducible.These numbers are characterised in terms of the positions of their ones.Further, the number of irreducible positive integers below a given bound is considered and evaluated asymptotically, as the bound goes to infinity.The periodic function that appears is analysed in detail.