cp's OEIS Frontend

A243650 Nonnegative integers of the form x^2+xy+12y^2.

%I A243650 #6 Jun 08 2014 16:07:53
%S A243650 0,1,4,9,12,14,16,18,24,25,32,36,42,47,48,49,51,54,56,63,64,68,72,81,
%T A243650 83,84,96,100,102,106,108,111,112,118,121,122,126,128,136,144,147,148,
%U A243650 162,168,169,178,188,189,191,192,194,196,197,204,213,216,222,224,225,237,238,243,252,256,262,269
%N A243650 Nonnegative integers of the form x^2+xy+12y^2.
%C A243650 Discriminant -47.
%H A243650 N. J. A. Sloane et al., <a href="https://oeis.org/wiki/Binary_Quadratic_Forms_and_OEIS">Binary Quadratic Forms and OEIS</a> (Index to related sequences, programs, references)
%p A243650 fd:=proc(a,b,c,M) local dd,xlim,ylim,x,y,t1,t2,t3,t4,i;
%p A243650 dd:=4*a*c-b^2;
%p A243650 if dd<=0 then error "Form should be positive definite."; break; fi;
%p A243650 t1:={};
%p A243650 xlim:=ceil( sqrt(M/a)*(1+abs(b)/sqrt(dd)));
%p A243650 ylim:=ceil( 2*sqrt(a*M/dd));
%p A243650 for x from 0 to xlim do
%p A243650 for y from -ylim to ylim do
%p A243650 t2 := a*x^2+b*x*y+c*y^2;
%p A243650 if t2 <= M then t1:={op(t1),t2}; fi; od: od:
%p A243650 t3:=sort(convert(t1,list));
%p A243650 t4:=[];
%p A243650 for i from 1 to nops(t3) do
%p A243650 if isprime(t3[i]) then t4:=[op(t4),t3[i]]; fi; od:
%p A243650 [[seq(t3[i],i=1..nops(t3))], [seq(t4[i],i=1..nops(t4))]];
%p A243650 end;
%p A243650 fd(1,1,12,500);
%Y A243650 Primes: A033232.
%K A243650 nonn
%O A243650 0,3
%A A243650 _N. J. A. Sloane_, Jun 08 2014