The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A325070 Prime numbers congruent to 9 modulo 16 representable by x^2 + 64*y^2. 3
 73, 89, 233, 281, 601, 617, 937, 1033, 1049, 1097, 1193, 1289, 1433, 1481, 1609, 1721, 1753, 1801, 1913, 2089, 2281, 2393, 2441, 2473, 2857, 2969, 3049, 3257, 3449, 3529, 3673, 3833, 4057, 4153, 4201, 4217, 4297, 4409, 4457, 4937, 5081, 5113, 5209, 5689, 5737 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Kaplansky showed that prime numbers congruent to 9 modulo 16 are representable by exactly one of the quadratic forms x^2 + 32*y^2 or x^2 + 64*y^2. A325069 corresponds to those representable by the first form and this sequence to those representable by the second form. LINKS David Brink, Five peculiar theorems on simultaneous representation of primes by quadratic forms, Journal of Number Theory 129(2) (2009), 464-468, doi:10.1016/j.jnt.2008.04.007, MR 2473893. Rémy Sigrist, PARI program for A325070 Wikipedia, Kaplansky's theorem on quadratic forms EXAMPLE Regarding 4201: - 4201 is a prime number, - 4201 = 262*16 + 9, - 4201 = 51^2 + 64*5^2, - hence 4201 belongs to this sequence. PROG (PARI) See Links section. CROSSREFS See A325067 for similar results. Cf. A105126, A325069. Sequence in context: A014754 A007766 A065111 * A152308 A072052 A333391 Adjacent sequences:  A325067 A325068 A325069 * A325071 A325072 A325073 KEYWORD nonn AUTHOR Rémy Sigrist, Mar 27 2019 STATUS approved

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

Last modified October 28 11:10 EDT 2020. Contains 338054 sequences. (Running on oeis4.)