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A243650 Nonnegative integers of the form x^2+xy+12y^2. 1
0, 1, 4, 9, 12, 14, 16, 18, 24, 25, 32, 36, 42, 47, 48, 49, 51, 54, 56, 63, 64, 68, 72, 81, 83, 84, 96, 100, 102, 106, 108, 111, 112, 118, 121, 122, 126, 128, 136, 144, 147, 148, 162, 168, 169, 178, 188, 189, 191, 192, 194, 196, 197, 204, 213, 216, 222, 224, 225, 237, 238, 243, 252, 256, 262, 269 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Discriminant -47.

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(1, 1, 12, 500);

CROSSREFS

Primes: A033232.

Sequence in context: A010413 A112652 A272933 * A140399 A312849 A161544

Adjacent sequences:  A243647 A243648 A243649 * A243651 A243652 A243653

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 08 2014

STATUS

approved

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Last modified April 22 13:29 EDT 2021. Contains 343177 sequences. (Running on oeis4.)