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A325076 Prime numbers congruent to 1, 16 or 22 modulo 39 neither representable by x^2 + x*y + 10*y^2 nor by x^2 + x*y + 127*y^2. 3

%I

%S 61,79,211,313,373,601,757,859,919,937,1069,1093,1303,1327,1543,1621,

%T 1699,1777,1873,2083,2089,2161,2239,2341,2551,2707,2713,2731,2791,

%U 2887,3019,3331,3571,3727,3823,4057,4273,4423,4507,4657,4813,4969,4993,5209,5227

%N Prime numbers congruent to 1, 16 or 22 modulo 39 neither representable by x^2 + x*y + 10*y^2 nor by x^2 + x*y + 127*y^2.

%C Brink showed that prime numbers congruent to 1, 16 or 22 modulo 39 are representable by both or neither of the quadratic forms x^2 + x*y + 10*y^2 and x^2 + x*y + 127*y^2. A325075 corresponds to those representable by both, and this sequence corresponds to those representable by neither.

%H David Brink, <a href="https://doi.org/10.1016/j.jnt.2008.04.007">Five peculiar theorems on simultaneous representation of primes by quadratic forms</a>, Journal of Number Theory 129(2) (2009), 464-468, doi:10.1016/j.jnt.2008.04.007, MR 2473893.

%H Rémy Sigrist, <a href="/A325076/a325076.gp.txt">PARI program for A325076</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Kaplansky%27s_theorem_on_quadratic_forms">Kaplansky's theorem on quadratic forms</a>

%e Regarding 61:

%e - 61 is a prime number,

%e - 61 = 39 + 22,

%e - 61 is neither representable by x^2 + x*y + 10*y^2 nor by x^2 + x*y + 127*y^2,

%e - hence 61 belongs to this sequence.

%o (PARI) See Links section.

%Y See A325067 for similar results.

%Y Cf. A325075.

%K nonn

%O 1,1

%A _Rémy Sigrist_, Mar 28 2019

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Last modified February 29 09:35 EST 2020. Contains 332355 sequences. (Running on oeis4.)