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A243681 Nonnegative integers of the form 3x^2+3xy+4y^2. 1
0, 3, 4, 10, 12, 13, 16, 22, 25, 27, 30, 36, 40, 48, 52, 55, 61, 64, 66, 75, 79, 82, 88, 90, 94, 100, 108, 117, 118, 120, 121, 127, 129, 130, 142, 144, 147, 156, 160, 165, 166, 172, 178, 192, 196, 198, 199, 205, 208, 211, 220, 225, 235, 243, 244, 246, 250, 256, 264, 270, 274, 282, 283, 286, 295, 298 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Discriminant -39.

LINKS

Table of n, a(n) for n=0..65.

N. J. A. Sloane et al., Binary Quadratic Forms and OEIS (Index to related sequences, programs, references)

MAPLE

fd:=proc(a, b, c, M) local dd, xlim, ylim, x, y, t1, t2, t3, t4, i;

dd:=4*a*c-b^2;

if dd<=0 then error "Form should be positive definite."; break; fi;

t1:={};

xlim:=ceil( sqrt(M/a)*(1+abs(b)/sqrt(dd)));

ylim:=ceil( 2*sqrt(a*M/dd));

for x from 0 to xlim do

for y from -ylim to ylim do

t2 := a*x^2+b*x*y+c*y^2;

if t2 <= M then t1:={op(t1), t2}; fi; od: od:

t3:=sort(convert(t1, list));

t4:=[];

for i from 1 to nops(t3) do

if isprime(t3[i]) then t4:=[op(t4), t3[i]]; fi; od:

[[seq(t3[i], i=1..nops(t3))], [seq(t4[i], i=1..nops(t4))]];

end;

fd(3, 3, 4, 500);

MATHEMATICA

Take[Union[3First[#]^2+3(Times@@#)+4Last[#]^2&/@Tuples[Range[-10, 10], 2]], 70] (* Harvey P. Dale, Jul 25 2014 *)

CROSSREFS

Primes: A106884.

Sequence in context: A131179 A079353 A242654 * A242881 A287448 A325235

Adjacent sequences:  A243678 A243679 A243680 * A243682 A243683 A243684

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 08 2014

STATUS

approved

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Last modified July 7 14:34 EDT 2020. Contains 335495 sequences. (Running on oeis4.)