Infinitive Sequence

A sequence $\{x_n\}$ is called an infinitive sequence if, for every $i$, $x_n=i$ for infinitely many $n$. Write $a(i,j)$ for the $j$th index $n$ for which $x_n=i$. Then as $i$ and $j$ range through $N$, the array $A=a(i,j)$, called the associative array of $x$, ranges through all of $N$.

See also Fractal Sequence

References

Kimberling, C. ``Fractal Sequences and Interspersions.'' Ars Combin. 45, 157-168, 1997.