Numerical Analogues of Aronson's Sequence
Number Theory
2014-09-17 v1 Information Theory
math.IT
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.
Keywords
Cite
@article{arxiv.math/0305308,
title = {Numerical Analogues of Aronson's Sequence},
author = {Benoit Cloitre and N. J. A. Sloane and Matthew J. Vandermast},
journal= {arXiv preprint arXiv:math/0305308},
year = {2014}
}
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16 pages