[seqfan] Re: True-False text sequence

Tanya Khovanova mathoflove-seqfan at yahoo.com
Mon Jan 23 02:20:38 CET 2012


I think that the bound sequence deserves to be in the OEIS too:

It starts as 1 2 3 4 4 5 6 6 7 7 8 8 8 9 10 10

and it is related to  A000788:
a(n) = the smallest k such that A000788(k) >= n-1.



________________________________
 From: Charles Greathouse <charles.greathouse at case.edu>
To: Sequence Fanatics Discussion list <seqfan at list.seqfan.eu> 
Sent: Wednesday, January 18, 2012 4:20 PM
Subject: [seqfan] True-False text sequence
 
Tanya Khovanova has two blog entries
http://blog.tanyakhovanova.com//?p=386
http://blog.tanyakhovanova.com/?p=387
discussing a sequence.  Is this (or a translate) in the OEIS?  If not,
would someone add it?

Quick definition: a(n) is the least number of guesses needed, in the
worst case, to find all the answers to an n-question true-or-false
test, where a guess consists of answering each question and learning
the total number of correct guesses.  This is related to Bulls and
Cows (aka Mastermind).

Knop and Mednikov prove upper bounds on the non-adaptive version,
which of course give upper bounds on the adaptive version as well.
Probably both should be in the OEIS.  The text of their paper is in
Russian,
http://www.mccme.ru/free-books/matpros/mpe.pdf
The paper is in Russian, and despite some work at Gould's text I'm not
able to read it.  There may be more results (or references) beside the
one Tanya mentions.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University

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