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

 

Logo

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 56th year, we are closing in on 350,000 sequences, and we’ve crossed 9,700 citations (which often say “discovered thanks to the OEIS”).

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A139668 Primes of the form x^2 + 1848*y^2. 6
1873, 2017, 2137, 2377, 2473, 2689, 3217, 3529, 3697, 4057, 4657, 5569, 6073, 6337, 7177, 7393, 7417, 7561, 7681, 7753, 8017, 8089, 8233, 8353, 8737, 8761, 9241, 9601, 9769, 11113, 11257, 11617, 12049, 12433, 12457, 12721, 13297, 13633, 13729, 14281, 15073, 15313, 16417, 16633, 16657, 16921, 16993, 17257, 17977, 18313, 18481, 19009, 19273, 19441, 20113 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Discriminant = -7392.

The primes are congruent to {1, 25, 169, 289, 361, 529, 625, 697, 793, 841, 961, 1345, 1369, 1633, 1681} (mod 1848).

More than the usual number of terms are shown in order to display the difference from A244019. - N. J. A. Sloane, Jun 19 2014

LINKS

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

William C. Jagy and Irving Kaplansky, Positive definite binary quadratic forms that represent the same primes [Cached copy]

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

MAPLE

fd:=proc(a, b, c, M) local dd, xlim, ylim, x, y, t1, t2, t3, t4, i;

dd:=4*a*c-b^2;

if dd<=0 then error "Form should be positive definite."; break; fi;

t1:={};

xlim:=ceil( sqrt(M/a)*(1+abs(b)/sqrt(dd)));

ylim:=ceil( 2*sqrt(a*M/dd));

for x from 0 to xlim do

for y from -ylim to ylim do

t2 := a*x^2+b*x*y+c*y^2;

if t2 <= M then t1:={op(t1), t2}; fi; od: od:

t3:=sort(convert(t1, list));

t4:=[];

for i from 1 to nops(t3) do

   if isprime(t3[i]) then t4:=[op(t4), t3[i]]; fi; od:

[[seq(t3[i], i=1..nops(t3))], [seq(t4[i], i=1..nops(t4))]];

end;

fd(1, 0, 1848, 50000); # N. J. A. Sloane, Jun 19 2014

MATHEMATICA

QuadPrimes2[1, 0, 1848, 10000] (* see A106856 *)

PROG

(MAGMA) [ p: p in PrimesUpTo(15000) | p mod 1848 in {1, 25, 169, 289, 361, 529, 625, 697, 793, 841, 961, 1345, 1369, 1633, 1681}]; // Vincenzo Librandi, Jul 29 2012

(MAGMA) k:=1848; [p: p in PrimesUpTo(21000) | NormEquation(k, p) eq true]; // Bruno Berselli, Jun 01 2016

CROSSREFS

Cf. A244019 (a different sequence which agrees for the first 43 terms), A106856.

Sequence in context: A270244 A154675 A068281 * A244019 A054818 A127410

Adjacent sequences:  A139665 A139666 A139667 * A139669 A139670 A139671

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 December 8 17:01 EST 2021. Contains 349596 sequences. (Running on oeis4.)