login
This site is supported by donations to The OEIS Foundation.

 

Logo

Invitation: celebrating 50 years of OEIS, 250000 sequences, and Sloane's 75th, there will be a conference at DIMACS, Rutgers, Oct 9-10 2014.

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A033203 Primes p congruent to {1, 2, 3} mod 8; or primes p of form x^2+2*y^2; or primes p such that x^2 = -2 has a solution mod p. 22
2, 3, 11, 17, 19, 41, 43, 59, 67, 73, 83, 89, 97, 107, 113, 131, 137, 139, 163, 179, 193, 211, 227, 233, 241, 251, 257, 281, 283, 307, 313, 331, 337, 347, 353, 379, 401, 409, 419, 433, 443, 449, 457, 467, 491, 499, 521, 523 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

If p>2 is a member then it has a unique representation as x^2+2y^2 [Frei, Theorem 3]. - N. J. A. Sloane, May 30 2014

Sequence naturally partitions into two sequences: all primes p with ord_p(-2) odd (A163183, the primes dividing 2^j +1 for some odd j) and certain primes p with ord_p(-2) even (A163185). [From Christopher J. Smyth, Jul 23 2009]

Terms m in A047476 with A010051(m) = 1. - Reinhard Zumkeller, Dec 29 2012

REFERENCES

David A. Cox, "Primes of the Form x^2 + n y^2", Wiley, 1989.

G. Frei, Euler's convenient numbers, Math. Intell. Vol. 7, No. 3 (1985), 55-58 and 64.

LINKS

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

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

FORMULA

a(n) = A002332(n) + 2*A002333(n)^2. - Zak Seidov, May 29 2014

MATHEMATICA

QuadPrimes2[1, 0, 2, 10000] (* see A106856 *)

Select[Prime[Range[200]], MemberQ[{1, 2, 3}, Mod[#, 8]]&] (* Harvey P. Dale, Mar 16 2013 *)

PROG

(Haskell)

a033203 n = a033203_list !! (n-1)

a033203_list = filter ((== 1) . a010051) a047476_list

-- Reinhard Zumkeller, Dec 29 2012, Jan 22 2012

(MAGMA) [p: p in PrimesUpTo(600) | p mod 8 in [1..3]]; // Vincenzo Librandi, Aug 11 2012

CROSSREFS

Cf. A033200.

Cf. A039706, A003628 (complement with respect to A000040).

Cf. A002332, A002333. - Zak Seidov, May 29 2014

Primes in A002479.

Sequence in context: A091734 A038902 A019355 * A051100 A051088 A051092

Adjacent sequences:  A033200 A033201 A033202 * A033204 A033205 A033206

KEYWORD

nonn,nice,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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

Content is available under The OEIS End-User License Agreement .

Last modified September 16 03:31 EDT 2014. Contains 246794 sequences.