×

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

Software:

OEIS
PDF BibTeX XML Cite
Full Text: arXiv EuDML EMIS