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
KEYWORD
nonn,easy
AUTHOR
T. D. Noe, Apr 29 2008
STATUS
approved