cp's OEIS Frontend

A243194 Nonnegative integers of the form x^2+xy+10y^2.

%I A243194 #7 Mar 07 2023 08:46:08
%S A243194 0,1,4,9,10,12,16,22,25,30,36,39,40,43,48,49,52,55,64,66,75,81,82,88,
%T A243194 90,94,100,103,108,118,120,121,130,139,142,144,156,157,160,165,166,
%U A243194 169,172,178,181,183,192,196,198,205,208,220,225,235,237,244,246,250,256,264,270,274,277,282,286,289
%N A243194 Nonnegative integers of the form x^2+xy+10y^2.
%C A243194 Discriminant -39.
%H A243194 Jean-François Alcover, <a href="/A243194/b243194.txt">Table of n, a(n) for n = 0..1611</a>
%H A243194 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 A243194 fd:=proc(a,b,c,M) local dd,xlim,ylim,x,y,t1,t2,t3,t4,i;
%p A243194 dd:=4*a*c-b^2;
%p A243194 if dd<=0 then error "Form should be positive definite."; break; fi;
%p A243194 t1:={};
%p A243194 xlim:=ceil( sqrt(M/a)*(1+abs(b)/sqrt(dd)));
%p A243194 ylim:=ceil( 2*sqrt(a*M/dd));
%p A243194 for x from 0 to xlim do
%p A243194 for y from -ylim to ylim do
%p A243194 t2 := a*x^2+b*x*y+c*y^2;
%p A243194 if t2 <= M then t1:={op(t1),t2}; fi; od: od:
%p A243194 t3:=sort(convert(t1,list));
%p A243194 t4:=[];
%p A243194 for i from 1 to nops(t3) do
%p A243194    if isprime(t3[i]) then t4:=[op(t4),t3[i]]; fi; od:
%p A243194 [[seq(t3[i],i=1..nops(t3))], [seq(t4[i],i=1..nops(t4))]];
%p A243194 end;
%p A243194 fd(1,1,10,500);
%t A243194 Module[{k, r}, Reap[For[k = 0, k <= 1000, k++, r = Reduce[k == x^2 + x y + 10 y^2, {x, y}, Integers]; If[r =!= False,(* Print[k," ",r]; *) Sow[k]]]][[2, 1]]] (* _Jean-François Alcover_, Mar 07 2023 *)
%Y A243194 Primes: A033227.
%K A243194 nonn
%O A243194 0,3
%A A243194 _N. J. A. Sloane_, Jun 08 2014