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Numerical Analogues of Aronson's Sequence

Benoit Cloitre·N. J. A. Sloane·Matthew J. Vandermast
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Abstract

Aronson's sequence 1, 4, 11, 16, ... is defined by the English sentence ``t is the first, fourth, eleventh, sixteenth, ... 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 >= 1. There are many generalizations of this sequence, some of which are new, while others throw new light on previously known sequences.

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BibTeXRIS

Benoit Cloitre, N. J. A. Sloane, Matthew J. Vandermast. 2003-05-21. Numerical Analogues of Aronson's Sequence. https://arxiv.org/abs/math/0305308

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