Geodesic
Numerical analogues of Aronson's sequence
Journal of integer sequences, Tome 6 (2003) no. 2
Aronson's sequence 1, 4, 11, 16,$ \dots $is defined by the English sentence "t is the first, fourth, eleventh, sixteenth,$ \dots $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.
Classification : 11B37
Keywords: self-describing sequence, aronson sequence, square of sequence (Concerned with sequences A079313 
@article{JIS_2003__6_2_a6,
     author = {Cloitre,  Benoit and Sloane,  N. J. A. and Vandermast,  Matthew J.},
     title = {Numerical analogues of {Aronson's} sequence},
     journal = {Journal of integer sequences},
     year = {2003},
     volume = {6},
     number = {2},
     zbl = {1142.11310},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2003__6_2_a6/}
}
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Cloitre,  Benoit; Sloane,  N. J. A.; Vandermast,  Matthew J. Numerical analogues of Aronson's sequence. Journal of integer sequences, Tome 6 (2003) no. 2. http://geodesic.mathdoc.fr/item/JIS_2003__6_2_a6/