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Numbers of the form x^2 + 4*y^2.
16

%I #42 Sep 08 2022 08:44:45

%S 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 72,73,80,81,85,89,97,100,101,104,109,113,116,117,121,125,128,136,137,

%U 144,145,148,149,153,157,160,164,169,173,180,181,185,193,196,197,200,205,208

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

%C x^2 + 4y^2 has discriminant -16.

%C 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 A004531(n) is nonzero if and only if n is of the form x^2 + 4*y^2. - _Michael Somos_, Jan 05 2012

%C 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 Jean-Christophe Hervé, <a href="/A020668/b020668.txt">Table of n, a(n) for n = 1..7500</a>

%H 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 Complement of A097269 in A001481. - _Jean-Christophe Hervé_, Oct 25 2015

%t Select[Range[0, 300], SquaresR[2, #] != 0 && Mod[#, 4] != 2&] (* _Jean-François Alcover_, May 13 2017 *)

%o (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 (Magma) [n: n in [0..208] | NormEquation(4, n) eq true]; // _Arkadiusz Wesolowski_, May 11 2016

%Y Cf. A001481, A004531, A042965, A097269. For primes see A002144.

%K easy,nonn

%O 1,3

%A _David W. Wilson_