# [seqfan] Re: True-False text sequence

David Wilson davidwwilson at comcast.net
Sat Mar 3 02:15:28 CET 2012

```On 1/22/2012 8:20 PM, Tanya Khovanova wrote:

Tanya describes the sequence

a(n) = smallest k with A000788(k) >= n-1.

for which she gets

1,2,3,4,4,5,6,6,7,7,8,8,8,9,10,10,...

whereas I get

0,1,2,3,3,4,5,5,6,6,7,7,7,8,9,9,10,10,...

(I presume we are both indexing starting at 1).

Tanya's sequence is 1 larger than mine at each element. My sequence is
essentially A100922.

Tanya's sequence could arguably be an upper bound in the test-taking
puzzle, mine could not, since in mine, a(1) = 0, and you need to take a
1-question test at least once to know the answers.

Perhaps someone can sort this out.

> 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,
>
> 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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```