Original scientific paper

Some properties of a function studied by De Rham, Carlitz and Dijkstra and its relation to the (Eisenstein-)Stern's diatomic sequence

I. Urbiha

Abstract

We present a novel approach to a remarkable function
D: N_0→N_0 defined by D(0)=0, D(1)=1, D(2n)=D(n), D(2n+1)=D(n)+D(n+1), studied independently by well known researchers in different areas of mathematics and computer science. Besides some
known properties we add some new ones (including a relation to the
(Eisenstein-)Stern's diatomic sequence). Some historical remarks are added at the end of this paper.

Keywords

recurrences; reduced fractions; continuants; (hyper) binary representation; Stern's diatomic sequence; 2-adic order; Stern-Brocot tree; Jacobsthal's numbers

Hrčak ID:

826

URI

https://hrcak.srce.hr/826

Publication date:

20.12.2001.

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