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Primes of the form 4x^2-4xy+7y^2, with x and y nonnegative.
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%I #43 Jul 12 2018 08:04:05

%S 7,31,79,103,127,151,199,223,271,367,439,463,487,607,631,727,751,823,

%T 919,967,991,1039,1063,1087,1231,1279,1303,1327,1399,1423,1447,1471,

%U 1543,1567,1663,1759,1783,1831,1879,1951,1999,2143,2239,2287,2311

%N Primes of the form 4x^2-4xy+7y^2, with x and y nonnegative.

%C Discriminant=-96.

%C Also, primes of the form 24n+7. - _Artur Jasinski_, Nov 25 2007 [See the Reble link]

%C Also primes of the forms 4x^2+4xy+7y^2, 7x^2+6xy+15y^2, 7x^2+2xy+7y^2 and 7x^2+4xy+28y^2. See A140633. - _T. D. Noe_, May 19 2008

%C Also, primes of form u^2+6v^2 with odd v while sequence A107008 is even v. This can be seen by expressing its form as (2x-y)^2+6y^2 (where y can only be odd) while the latter is x^2+6(2y)^2. Additionally, this sequence is 7 mod 24 while the second is 1 mod 24 and together, they are the primes of form x^2+6y^2 (A033199) which are either {1,7} mod 24. - _Tito Piezas III_, Jan 01 2009

%H Vincenzo Librandi, N. J. A. Sloane and Ray Chandler, <a href="/A107006/b107006.txt">Table of n, a(n) for n = 1..10000</a> [First 1000 terms from Vincenzo Librandi, next 168 terms from N. J. A. Sloane]

%H Don Reble, <a href="/A107006/a107006.txt">Notes on this sequence</a>

%H J. Liouville, <a href="http://sites.mathdoc.fr/JMPA/afficher_notice.php?id=JMPA_1859_2_4_A36_0">Théorème concernant les nombres premiers de la forme 24µ + 7</a>, Journal de mathématiques pures et appliquées 2e série, tome 4 (1859), pp. 399-400.

%H N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)

%t a = {}; Do[If[PrimeQ[24n + 7], AppendTo[a, 24n + 7]], {n, 0, 100}]; a (* _Artur Jasinski_, Nov 25 2007 *)

%t QuadPrimes2[4, -4, 7, 10000] (* see A106856 *)

%t Select[24*Range[0,4000]+7,PrimeQ] (* _Harvey P. Dale_, May 13 2018 *)

%Y Cf. A124477.

%K nonn,easy

%O 1,1

%A _T. D. Noe_, May 09 2005

%E Recomputed b-file and deleted erroneous Mma program by _N. J. A. Sloane_, Jun 08 2014