Aronson's sequence
Aronson's sequence is a sequence of numbers that is defined to make the sentence "T is the first, fourth, eleventh, ... letter in this sentence, not counting spaces or commas" true.
In Douglas Hofstadter's book Metamagical Themas, the sequence is credited to J. K. Aronson of Oxford, England; it is based on the observation that ordinal numbers in the English language always end in "th".[1]
The first few numbers in the sequence are:
Aronson's sequence is essentially an autogram that describes itself. Cloitre, Sloane & Vandermast (2003) write that Aronson's sequence is "a classic example of a self-referential sequence"; however, they criticize it for being ambiguously defined due to the variation in naming of numbers over one hundred in different dialects of English. In its place, they offer several other self-referential sequences whose definitions rely only on mathematics rather than on the English language.[2]
References
- ^ Hofstadter, Douglas R. (1996), Metamagical Themas: Questing For The Essence Of Mind And Pattern, Basic Books, p. 44, ISBN 9780465045662.
- ^ Cloitre, Benoit; Sloane, N. J. A.; Vandermast, Matthew J. (2003), "Numerical analogues of Aronson's sequence" (PDF), Journal of Integer Sequences, 6, Art. 03.2.2, arXiv:math/0305308.