A sequence of positive integers is called an iteration sequence if there exists a strictly increasing sequence of positive integers such that and for , 3, .... A necessary and sufficient condition for to be an iteration sequence is

for all .

Kimberling, C. "Interspersions and Dispersions." Proc. Amer. Math. Soc. 117, 313-321, 1993.

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Weisstein, Eric W. "Iteration Sequence." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/IterationSequence.html