[seqfan] Re: Primes of the form 8n + 7 or -x + 4xy + 4y^2
njasloane at gmail.com
Sun Nov 13 20:33:12 CET 2016
Al, I agree with your reasoning, and I will edit the two sequences as you
Neil J. A. Sloane, President, OEIS Foundation.
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On Sun, Nov 13, 2016 at 2:23 PM, Alonso Del Arte <alonso.delarte at gmail.com>
> I am now convinced that A007522, primes of the form 8n + 7, and A141175,
> primes of the form -x + 4xy + 4y^2, are indeed the same sequence.
> If both x and y are even, then it doesn't matter, -x + 4xy + 4y^2 gives us
> a composite even number. If x is even but y is odd then the formula still
> gives us a composite even number.
> If y is even, then 4xy + 4y^2 is a multiple of 8. With y even and x odd, we
> see that x^2 = 1 mod 8, which "flips over" to -x^2 = 7 mod 8. Therefore,
> primes of the form -x + 4xy + 4y^2 are a trivial, not proper, subset of
> primes of the form 8n + 7.
> This is correct and complete, right? Given that A141175 has been in the
> OEIS for almost a decade, it should be labeled a duplicate and have its
> relevant information not already in A007522 copied over to the older entry?
> Alonso del Arte
> Author at SmashWords.com
> Musician at ReverbNation.com <http://www.reverbnation.com/alonsodelarte>
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