|Journal of Integer Sequences, Vol. 6 (2003), Article 03.2.2|
N. J. A. Sloane
AT\&T Shannon Labs
Florham Park, NJ 07932-0971
Matthew J. Vandermast
53 Piaget Avenue
Clifton, NJ 07011-1216
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.
(Concerned with sequences A005224 A001462 A079000 A079948 A080596 A079313 A079253 A081023 A080653 A079325 A079257 A079258 A079254 A014132 A000217 A003605 A006166 A080637 A079882 A007378 A080780 A080588 A080591 A000201 A080760 A010906 A080759 A080746 A079255 A079259 .)
Received March 31, 2003; revised version received July 2, 2003. Published in Journal of Integer Sequences July 4, 2003.