cp's OEIS Frontend

A244037 Numbers of the form x^2+14y^2.

%I A244037 #12 Feb 08 2023 07:22:19
%S A244037 0,1,4,9,14,15,16,18,23,25,30,36,39,49,50,56,57,60,63,64,65,72,78,81,
%T A244037 92,95,100,105,114,120,121,126,127,130,135,137,142,144,151,156,158,
%U A244037 162,169,175,177,183,190,196,200,207,210,224,225,226,228,233,239,240,247,249,252,256,260,270,273,281
%N A244037 Numbers of the form x^2+14y^2.
%H A244037 Robert Israel, <a href="/A244037/b244037.txt">Table of n, a(n) for n = 1..10000</a>
%H A244037 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 A244037 fd:=proc(a,b,c,M) local dd,xlim,ylim,x,y,t1,t2,t3,t4,i;
%p A244037 dd:=4*a*c-b^2;
%p A244037 if dd<=0 then error "Form should be positive definite."; break; fi;
%p A244037 t1:={};
%p A244037 xlim:=ceil( sqrt(M/a)*(1+abs(b)/sqrt(dd)));
%p A244037 ylim:=ceil( 2*sqrt(a*M/dd));
%p A244037 for x from 0 to xlim do
%p A244037 for y from -ylim to ylim do
%p A244037 t2 := a*x^2+b*x*y+c*y^2;
%p A244037 if t2 <= M then t1:={op(t1),t2}; fi; od: od:
%p A244037 t3:=sort(convert(t1,list));
%p A244037 t4:=[];
%p A244037 for i from 1 to nops(t3) do
%p A244037    if isprime(t3[i]) then t4:=[op(t4),t3[i]]; fi; od:
%p A244037 [[seq(t3[i],i=1..nops(t3))], [seq(t4[i],i=1..nops(t4))]];
%p A244037 end;
%p A244037 fd(1,0,14,500);
%p A244037 # Alternative:
%p A244037 N:= 1000: # for terms <= N
%p A244037 sort(convert({seq(seq(x^2+14*y^2, y=0..floor(sqrt((N-x^2)/14))),x=0..floor(sqrt(N)))},list)); # _Robert Israel_, Sep 30 2020
%t A244037 M = 1000; (* for terms <= M *)
%t A244037 Table[x^2 + 14 y^2, {x, 0, Floor@Sqrt[M]}, {y, 0, Floor@Sqrt[(M - x^2)/14]}] // Flatten // Union (* _Jean-François Alcover_, Feb 08 2023, after _Robert Israel_ *)
%Y A244037 For primes see A033211.
%K A244037 nonn
%O A244037 1,3
%A A244037 _N. J. A. Sloane_, Jun 28 2014