  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.
