login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual Appeal: Today, Nov 11 2014, is the 4th anniversary of the launch of the new OEIS web site. 70,000 sequences have been added in these four years, all edited by volunteers. Please make a donation (tax deductible in the US) to help keep the OEIS running.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..22.

S. Alexander, On Guessing Whether A Sequence Has A Certain Property, arXiv:1011.6626 [math.LO]

CROSSREFS

Sequence in context: A065883 A214392 A071975 * A197701 A242107 A242108

Adjacent sequences:  A182656 A182657 A182658 * A182660 A182661 A182662

KEYWORD

nonn

AUTHOR

Sam Alexander, Nov 26 2010

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified December 21 15:15 EST 2014. Contains 252323 sequences.