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 A182659 A canonical permutation designed to thwart a certain naive attempt to guess whether sequences are permutations. 1
 0, 2, 3, 1, 5, 6, 7, 8, 9, 4, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 10, 22 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS A naive way to guess whether a function f:N->N is a permutation, based on just an initial subsequence (f(0),...,f(n)), is to guess "no" if (f(0),...,f(n)) contains a repeated entry or if there is some i in {0,...,n} such that i is not in {f(0),...,f(n)} and 2 i<=n; and guess "yes" otherwise. a(n) thwarts that method, causing it to change its mind infinitely often as n->infinity. a(0)=0. Suppose a(0),...,a(n) have been defined. 1. If the above method guesses that (a(0),...,a(n)) is NOT an initial subsequence of a permutation, then unmark any "marked" numbers. 2. If the above method guesses that (a(0),...,a(n)) IS an initial subsequence of a permutation, then "mark" the smallest number not in {a(0),...,a(n)}. 3. Let a(n+1) be the least unmarked number not in {a(0),...,a(n)}. A030301 can be derived by a similar method, where instead of trying to guess whether sequences are permutations, the naive victim is trying to guess whether sequences contain infinitely many 0s. LINKS S. Alexander, On Guessing Whether A Sequence Has A Certain Property, arXiv:1011.6626 [math.LO], 2010-2012, J. Int. Seq. 14 (2011) # 11.4.4 CROSSREFS Cf. A030301. Sequence in context: A065883 A214392 A071975 * A197701 A292770 A242107 Adjacent sequences:  A182656 A182657 A182658 * A182660 A182661 A182662 KEYWORD nonn AUTHOR Sam Alexander, Nov 26 2010 STATUS approved

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Last modified September 20 17:42 EDT 2021. Contains 347588 sequences. (Running on oeis4.)