## Jacobsthal representation numbers.(English)Zbl 0869.11013

The author derives elementary properties of the sequences $J_{n+2} =J_{n+ 1} +2J_n,\;J_0=0,\;J_1=1,\;n\geq 0,\text{ and } j_{n+2} =j_{n+1} +2j_n,\;j_0= 2,\;j_1=1,\;n\geq 0,$ the Jacobsthal and Jacobsthal-Lucas sequences, respectively. He then shows that every positive integer $$N$$ has a representation $$N=\sum_{j\geq 1} a_jJ_{n+1}$$, where $$a_j\in \{0,1,2\}$$ and $$a_j =2 \Rightarrow a_{j+1} =0$$. A similar representation is also derived in terms of the sequence $$\{j_n\}$$.

### MSC:

 11B39 Fibonacci and Lucas numbers and polynomials and generalizations 11A67 Other number representations