[seqfan] Re: A261009

[jean-paul allouche]

Dear Neil

Many thanks!
best wishes
jean-paul

Le 25/10/15 08:30, Neil Sloane a écrit :
> Dear Jean-Paul, I added a comment to A261009, based on your message.
>
> (By the way, the line you quote in 3. is part of a Haskell program, I
> believe,
> which explains why it is hard to interpret!)
>
> Best regards
> Neil
>
> Neil J. A. Sloane, President, OEIS Foundation.
> 11 South Adelaide Avenue, Highland Park, NJ 08904, USA.
> Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ.
> Phone: 732 828 6098; home page: http://NeilSloane.com
> Email: njasloane at gmail.com
>
>
> On Sun, Oct 25, 2015 at 2:48 AM, jean-paul allouche <
> jean-paul.allouche at imj-prg.fr> wrote:
>
>> Dear Seqfans
>>
>> As recalled in http://www.integers-ejcnt.org/p43/p43.mail.html
>> [Integers: Powers in prime bases and a problem on central coefficients]
>> the following problem, cited in "Concrete Mathematics" by
>> Graham, Knuth, and Patashnik, is still open: prove that for all n > 256
>> one has that binom(2n,n) is either divisible by 4 or by 9.
>>
>> This can be easily reduced to: if c_n is the n-th term of A261009,
>> then for all k \geq 9, one has
>> 2c_k - c_{k+1} \geq 4.
>>
>> 1. This has been proved up to huge values of k (see ref. above where
>>      k = 10^{13} is indicated). This is certainly (as any base change
>> problem)
>>      a very difficult question... except if some ingenious trick would work:
>>      any idea?
>>
>> 2. This conjecture does not appear in A261009 on the OEIS.
>>
>> 3. The following appears about this sequence on the OEIS:
>>      "a261009 = a053735 . a000079  -- Reinhard Zumkeller, Aug 14 2015"
>>      I guess this should read "a261009 = a053735 composed with a000079"
>>      as indicated a few lines above:
>>      "a(n) = A053735(A000079(n)). - Michel Marcus, Aug 14 2015"
>>
>> Best wishes
>> jean-paul
>>
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