Aronson's sequence: Difference between revisions

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{{Short description|Sequence of numbers}}

'''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, ... {{OEIS|A005224}}.

In [[Douglas Hofstadter]]'s book ''[[Metamagical Themas]]'', the sequence is credited to [[Jeffrey 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 number (linguistics)|ordinal number]]s, except those that end in 2, must contain at least one "t".<ref>{{citation|title=Metamagical Themas: Questing For The Essence Of Mind And Pattern|first=Douglas R.|last=Hofstadter|authorlink=Douglas Hofstadter|publisher=Basic Books|year=1996|isbn=9780465045662|page=44|url=https://books.google.com/books?id=o8jzWF7rD6oC&pg=PA44}}.</ref>

Aronson's sequence is closely related to [[autogram]]s. There are many generalizations of Aronson's sequence and research into the topic is ongoing.<ref name=benoit/>

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| at = Art. 03.2.2

| title = Numerical analogues of Aronson's sequence

| url = http://www.emis.ams.orgde/journals/JIS/VOL6/Cloitre/cloitre2.pdf

| volume = 6

| issue = 2003

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== External links ==

* {{mathworld|urlname=AronsonsSequence|title=Aronson's Sequence}}

{{Classes of natural numbers}}

[[Category:Base-dependent integer sequences]]