Numerical Analogues of Aronson's Sequence
<|reference_start|>Numerical Analogues of Aronson's Sequence: 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.<|reference_end|>
@article{cloitre2003numerical,
    title={Numerical Analogues of Aronson's Sequence},
    author={Benoit Cloitre, N. J. A. Sloane, Matthew J. Vandermast},
    journal={J. Integer Sequences, 6 (2003), #03.2.2},
    year={2003},
    archivePrefix={arXiv},
    eprint={math/0305308},
    primaryClass={math.NT cs.IT math.IT}
}