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

Department of Mathematics, University of Osijek
Publication Date
  • Recurrences
  • Reduced Fractions
  • Continuants
  • (Hyper) Binary Representation
  • Stern'S Diatomic Sequence
  • 2-Adic Order
  • Stern-Brocot Tree
  • Jacobsthal'S Numbers
  • Computer Science
  • Mathematics


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.

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