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

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A139645 Primes of the form x^2 + 112*y^2. 3
113, 137, 193, 233, 281, 337, 401, 449, 457, 569, 617, 641, 673, 809, 953, 977, 1009, 1033, 1129, 1201, 1289, 1297, 1409, 1481, 1801, 1873, 1913, 2017, 2081, 2129, 2137, 2153, 2297, 2377, 2417, 2473, 2521, 2633, 2657, 2689, 2713, 2753, 2801 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Discriminant is -448. See A139643 for more information.

Primes of the form 8*n + 1 which cannot be expressed as 7*k - 1, 7*k - 2, or 7*k - 4. a(n)^3 == 1 (mod 56). - Gary Detlefs, Jan 26 2014

The primes are congruent to {1, 9, 25} (mod 56).

LINKS

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

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

MAPLE

f:=n-> ceil((8*n+1)/7)-(8*n+1): for n from 1 to 350 do if isprime(8*n+1) and f(n)<>1 and f(n)<>2 and f(n)<>4 then print(8*n+1) fi od. # Gary Detlefs, Jan 26 2014

MATHEMATICA

QuadPrimes2[1, 0, 112, 10000] (* see A106856 *)

PROG

(MAGMA) [ p: p in PrimesUpTo(3000) | p mod 56 in {1, 9, 25}]; // Vincenzo Librandi, Jul 28 2012

(MAGMA) k:=112; [p: p in PrimesUpTo(3000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

CROSSREFS

Sequence in context: A216288 A224554 A095617 * A240584 A139988 A140005

Adjacent sequences:  A139642 A139643 A139644 * A139646 A139647 A139648

KEYWORD

nonn,easy

AUTHOR

T. D. Noe, Apr 29 2008

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 July 20 22:20 EDT 2019. Contains 325189 sequences. (Running on oeis4.)