Aronson's sequence

Aronson's sequence is an integer sequence defined by the English sentence "T is the first, fourth, eleventh, sixteenth, ... letter in this sentence." Spaces and punctuation are ignored. The first few numbers in the sequence are:

1, 4, 11, 16, 24, 29, 33, 35, 39, 45, 47, 51, 56, 58, 62, 64, 69, 73, 78, 80, 84, 89, 94, 99, 104, 111, 116, 122, 126, 131, 136, 142, 147, 158, 164, 169, ... (sequence A005224 in the OEIS).

In Douglas Hofstadter's book Metamagical Themas, the sequence is credited to J. K. Aronson of Oxford, England. The sequence is infinite—and this statement requires some proof. The proof depends on the observation that the English names of all ordinal numbers, except those that end in 2, must contain at least one "t".[1]

Aronson's sequence is closely related to autograms . There are many generalizations of Aronson's sequence and research into the topic is ongoing.[2][3]

Cloitre & Sloane (Vandermast) 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

External links

This article is issued from Wikipedia - version of the 11/2/2016. The text is available under the Creative Commons Attribution/Share Alike but additional terms may apply for the media files.