The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A107006 Primes of the form 4x^2-4xy+7y^2, with x and y nonnegative. 16
 7, 31, 79, 103, 127, 151, 199, 223, 271, 367, 439, 463, 487, 607, 631, 727, 751, 823, 919, 967, 991, 1039, 1063, 1087, 1231, 1279, 1303, 1327, 1399, 1423, 1447, 1471, 1543, 1567, 1663, 1759, 1783, 1831, 1879, 1951, 1999, 2143, 2239, 2287, 2311 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Discriminant=-96. Also, primes of the form 24n+7. - Artur Jasinski, Nov 25 2007 [See the Reble link] 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 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 LINKS Vincenzo Librandi, N. J. A. Sloane and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi, next 168 terms from N. J. A. Sloane] Don Reble, Notes on this sequence J. Liouville, Théorème concernant les nombres premiers de la forme 24µ + 7, Journal de mathématiques pures et appliquées 2e série, tome 4 (1859), pp. 399-400. N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references) MATHEMATICA a = {}; Do[If[PrimeQ[24n + 7], AppendTo[a, 24n + 7]], {n, 0, 100}]; a (* Artur Jasinski, Nov 25 2007 *) QuadPrimes2[4, -4, 7, 10000] (* see A106856 *) Select[24*Range[0, 4000]+7, PrimeQ] (* Harvey P. Dale, May 13 2018 *) CROSSREFS Cf. A124477. Sequence in context: A033199 A304163 A003550 * A107005 A201477 A164621 Adjacent sequences: A107003 A107004 A107005 * A107007 A107008 A107009 KEYWORD nonn,easy AUTHOR T. D. Noe, May 09 2005 EXTENSIONS Recomputed b-file and deleted erroneous Mma program by N. J. A. Sloane, Jun 08 2014 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified May 29 11:04 EDT 2024. Contains 372938 sequences. (Running on oeis4.)