cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A107006 Primes of the form 4x^2-4xy+7y^2, with x and y nonnegative.

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%I A107006 #43 Jul 12 2018 08:04:05
%S A107006 7,31,79,103,127,151,199,223,271,367,439,463,487,607,631,727,751,823,
%T A107006 919,967,991,1039,1063,1087,1231,1279,1303,1327,1399,1423,1447,1471,
%U A107006 1543,1567,1663,1759,1783,1831,1879,1951,1999,2143,2239,2287,2311
%N A107006 Primes of the form 4x^2-4xy+7y^2, with x and y nonnegative.
%C A107006 Discriminant=-96.
%C A107006 Also, primes of the form 24n+7. - _Artur Jasinski_, Nov 25 2007 [See the Reble link]
%C A107006 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 A107006 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 A107006 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 A107006 Don Reble, <a href="/A107006/a107006.txt">Notes on this sequence</a>
%H A107006 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 A107006 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 A107006 a = {}; Do[If[PrimeQ[24n + 7], AppendTo[a, 24n + 7]], {n, 0, 100}]; a (* _Artur Jasinski_, Nov 25 2007 *)
%t A107006 QuadPrimes2[4, -4, 7, 10000] (* see A106856 *)
%t A107006 Select[24*Range[0,4000]+7,PrimeQ] (* _Harvey P. Dale_, May 13 2018 *)
%Y A107006 Cf. A124477.
%K A107006 nonn,easy
%O A107006 1,1
%A A107006 _T. D. Noe_, May 09 2005
%E A107006 Recomputed b-file and deleted erroneous Mma program by _N. J. A. Sloane_, Jun 08 2014