[seqfan] Re: A135064
Charles Greathouse
charles.greathouse at case.edu
Sat Mar 4 01:54:35 CET 2017
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.
>
> Cheers,
> Robert
>
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