## Numerical analogues of Aronson’s sequence.(English)Zbl 1142.11310

Summary: Aronson’s sequence 1, 4, 11, 16, $$\ldots$$ is defined by the English sentence “t is the first, fourth, eleventh, sixteenth, $$\ldots$$ letter of this sentence.” This paper introduces some numerical analogues, such as: $$a(n)$$ is taken to be the smallest positive integer greater than $$a(n-1)$$ which is consistent with the condition “$$n$$ is a member of the sequence if and only if $$a(n)$$ is odd.” This sequence can also be characterized by its “square”, the sequence $$a^{(2)} (n) = a(a(n))$$, which equals $$2n+3$$ for $$n \geq 1$$. There are many generalizations of this sequence, some of which are new, while others throw new light on previously known sequences.

### MSC:

 11B37 Recurrences

OEIS
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