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A243652
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Nonnegative integers of the form 2x^2+xy+6y^2.
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1
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0, 2, 6, 7, 8, 9, 12, 16, 18, 21, 24, 27, 28, 32, 34, 36, 42, 48, 50, 51, 53, 54, 56, 59, 61, 63, 64, 68, 72, 74, 81, 84, 89, 94, 96, 97, 98, 102, 108, 111, 112, 119, 126, 128, 131, 136, 142, 144, 147, 148, 150, 153, 157, 158, 159, 162, 166, 168, 173, 175, 177, 183, 189, 192, 196, 200, 202, 204, 206
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OFFSET
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0,2
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COMMENTS
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Discriminant -47.
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LINKS
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MAPLE
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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(2, 1, 6, 500);
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CROSSREFS
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Primes: 106898.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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