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Numbers of the form 3x^2+2xy+3y^2.
3

%I #10 Feb 10 2020 00:46:02

%S 0,3,4,8,11,12,16,19,24,27,32,36,43,44,48,51,59,64,67,68,72,75,76,83,

%T 88,96,99,100,107,108,123,128,131,132,136,139,144,147,152,163,164,171,

%U 172,176,179,187,192,196,200,204,211,216,219,227,228,236,243,251,256,264,267,268,272,275,283,288,291,292,300,304,307,323,324,328,331,332,339,344,347

%N Numbers of the form 3x^2+2xy+3y^2.

%C Discriminant -32.

%H Charles R Greathouse IV, <a href="/A243177/b243177.txt">Table of n, a(n) for n = 1..10000</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)

%H Naoki Uchida, <a href="https://arxiv.org/abs/2001.11632">Integers of the Form ax^2 + bxy + cy^2</a> (2020 preprint)

%t ofTheFormQ[n_] := Reduce[n == 3*x^2 + 2*x*y + 3*y^2, {x, y}, Integers] =!= False; Select[Range[0, 400], ofTheFormQ] (* _Jean-François Alcover_, Jun 04 2014 *)

%o (PARI) is(n)=if(n==0, return(1)); my(h=valuation(n,2),f=factor(n>>h),s); if(h==1, return(0)); for(i=1,#f~, if(f[i,1]%8==3, s+=f[i,2], f[i,1]%8>3 && f[i,2]%2, return(0))); h>1 || s%2 \\ _Charles R Greathouse IV_, Feb 10 2020

%Y Primes: A007520.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Jun 02 2014