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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

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Last modified July 20 23:29 EDT 2019. Contains 325189 sequences. (Running on oeis4.)