[seqfan] A135064

israel at math.ubc.ca israel at math.ubc.ca
Fri Mar 3 22:28:31 CET 2017

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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