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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A105389 Primes of the form x^2 + 32 y^2, also primes p with h(-p) divisible by 8. 3
41, 113, 137, 257, 313, 337, 353, 409, 457, 521, 569, 577, 593, 761, 809, 857, 881, 953, 1129, 1153, 1201, 1217, 1249, 1321, 1553, 1601, 1657, 1777, 1889, 1993 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Barrucand, P. and Cohn, H. Note on primes of the form x^2 + 32 y^2, class number and residuacity, Journal fur die reine und angewandte Mathematik, v.238, pp. 67-70.

LINKS

Vincenzo Librandi and Ray Chandler, Table of n, a(n) for n = 1..10000 [First 1000 terms from Vincenzo Librandi]

S. R. Finch, Powers of Euler's q-Series, arXiv:math/0701251 [math.NT], 2007.

Steven R. Finch, Class number theory [Cached copy, with permission of the author]

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

EXAMPLE

41 = 9 + 32 * 1, 113 = 81 + 32 *1, 137 = 9 + 32*4

MATHEMATICA

QuadPrimes2[1, 0, 32, 10000] (* see A106856 *)

(* Second program: *)

max = 10^4; Table[yy = {y, 1, Floor[Sqrt[(max - x^2)/32]]}; Table[x^2 + 32 y^2, yy // Evaluate], {x, 1, Floor[Sqrt[max]]}] // Flatten // Union // Select[#, # <= max && PrimeQ[#]&]& (* Jean-Fran├žois Alcover, Oct 04 2018 *)

CROSSREFS

Sequence in context: A070270 A001125 A116509 * A266954 A290589 A191867

Adjacent sequences:  A105386 A105387 A105388 * A105390 A105391 A105392

KEYWORD

nonn

AUTHOR

John L. Drost, May 01 2005

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.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 28 03:04 EDT 2020. Contains 334671 sequences. (Running on oeis4.)