[seqfan] Re: A135064
njasloane at gmail.com
Sat Mar 4 18:41:51 CET 2017
Charles, I suggest (concerning A135064) that we
1. cut back the terms that we show (in the data lines and the b-file) to
just those that you have verified from the definition
2. remove everything else except the conjecture
I will take care of this
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 Fri, Mar 3, 2017 at 7:54 PM, Charles Greathouse
<charles.greathouse at case.edu> wrote:
> I have not (yet?) attempted to prove the conjecture. I did check that it
> holds for n < 10^6 and that the first 500 terms of the sequence (209
> digits) generated by the recurrence correspond to polynomials with Galois
> group A5. Both of these rely on the PARI/GP polgalois command.
> Charles Greathouse
> Case Western Reserve University
> On Fri, Mar 3, 2017 at 4:28 PM, <israel at math.ubc.ca> wrote:
>> This sequence is "Numbers n such that the quintic polynomial x^5 -
>> 10*n*x^2 - 24*n has Galois group A_5 over rationals."
>> In 2007 Klaus Brockhaus commented "Sequence appears to agree with the
>> Lucas bisection A002878 for n > 1", and Neil commented "If this agreement
>> is provable then of course it provides recurrences, generating functions,
>> etc., for this sequence." A number of people appear to have ignored the
>> "if" clause and provided the recurrence, generating function, programs,
>> additional terms and b-file from that. At least, I doubt that anybody has
>> directly computed the Galois group for all n up to a(10000).
>> Joerg made a pink-box comment in September 2016 "Careful, so far this one
>> appears(1) to agree with A002878. SO all program should be removed and all
>> formulas need "conjecture" with them."
>> However this has not been done.
>> Is anybody able to prove the conjecture? If not, I agree with Joerg and we
>> need to do some editing.
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