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A242665 Nonnegative integers of the form -x^2 + 4xy + 2y^2.

%I A242665 #23 Jun 03 2022 18:09:04
%S A242665 0,2,5,6,8,15,18,20,23,24,29,32,38,45,47,50,53,54,60,69,71,72,80,86,
%T A242665 87,92,95,96,98,101,114,116,125,128,134,135,141,146,149,150,152,159,
%U A242665 162,167,173,180,188,191,194,197,200,207,212,213,215,216,230,239,240,242,245,258,261,263,269,276,278,284,285,288,290,293,294
%N A242665 Nonnegative integers of the form -x^2 + 4xy + 2y^2.
%C A242665 Discriminant 24.
%C A242665 Multiplied by -1, these are the nonpositive norms of numbers in Z[sqrt(6)]. - _Alonso del Arte_, Sep 26 2014
%C A242665 Nonnegative integers of the form 2*x^2 - 3*y^2. - _Robert Israel_, Jun 03 2018
%C A242665 Nonnegative integers of the form 6*x^2 - y^2. - _Jon E. Schoenfield_, Jun 03 2022
%H A242665 Robert Israel, <a href="/A242665/b242665.txt">Table of n, a(n) for n = 1..10000</a>
%H A242665 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 A242665 Math Stackexchange, <a href="https://math.stackexchange.com/questions/2806271/can-the-integers-n-expressible-as-2a2-3b2-be-classified">Can the integers n expressible as 2a^2-3b^2 be classified?</a>
%p A242665 filter:= proc(n) local F;
%p A242665   F:= map(proc(t) local p; p:= t[1] mod 24; if t[2]::even or member(p,{3,1,19}) then NULL else p fi end proc, ifactors(n)[2]);
%p A242665   if convert(F,set) intersect {7,11,13,17} <> {} then return false fi;
%p A242665   nops(F)::odd
%p A242665 end proc:
%p A242665 filter(0):= true:
%p A242665 select(filter, [$0..400]); # _Robert Israel_, Jun 03 2018
%t A242665 Reap[For[n = 0, n <= 300, n++, If[Reduce[-x^2 + 4*x*y + 2*y^2 == n, {x, y}, Integers] =!= False, Sow[n]]]][[2, 1]]
%Y A242665 Primes in this sequence = A141171.
%K A242665 nonn
%O A242665 1,2
%A A242665 _N. J. A. Sloane_, May 31 2014