cp's OEIS Frontend

A020668 Numbers of the form x^2 + 4*y^2.

%I A020668 #42 Sep 08 2022 08:44:45
%S A020668 0,1,4,5,8,9,13,16,17,20,25,29,32,36,37,40,41,45,49,52,53,61,64,65,68,
%T A020668 72,73,80,81,85,89,97,100,101,104,109,113,116,117,121,125,128,136,137,
%U A020668 144,145,148,149,153,157,160,164,169,173,180,181,185,193,196,197,200,205,208
%N A020668 Numbers of the form x^2 + 4*y^2.
%C A020668 x^2 + 4y^2 has discriminant -16.
%C A020668 Numbers that can be expressed as both the sum of two squares and the difference of two squares; the intersection of sequences A001481 and A042965. - _T. D. Noe_, Feb 05 2003
%C A020668 A004531(n) is nonzero if and only if n is of the form x^2 + 4*y^2. - _Michael Somos_, Jan 05 2012
%C A020668 These are the sum of two squares that are congruent to 0 or 1 (mod 4), and thus that are also the difference of two squares. - _Jean-Christophe Hervé_, Oct 25 2015
%H A020668 Jean-Christophe Hervé, <a href="/A020668/b020668.txt">Table of n, a(n) for n = 1..7500</a>
%H A020668 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)
%F A020668 Complement of A097269 in A001481. - _Jean-Christophe Hervé_, Oct 25 2015
%t A020668 Select[Range[0, 300], SquaresR[2, #] != 0 && Mod[#, 4] != 2&] (* _Jean-François Alcover_, May 13 2017 *)
%o A020668 (PARI) for(n=0, 1e3, if(if( n<1, n==0, 2 * qfrep([ 1, 0; 0, 4], n)[n]) != 0, print1(n, ", "))) \\ _Altug Alkan_, Oct 29 2015
%o A020668 (Magma) [n: n in [0..208] | NormEquation(4, n) eq true]; // _Arkadiusz Wesolowski_, May 11 2016
%Y A020668 Cf. A001481, A004531, A042965, A097269. For primes see A002144.
%K A020668 easy,nonn
%O A020668 1,3
%A A020668 _David W. Wilson_