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A152411 Nonnegative integers representable as m^2 - n^4 for positive integers m,n.

%I A152411 #15 Jul 24 2020 15:58:47
%S A152411 0,3,8,9,15,19,20,24,33,35,40,48,51,63,65,68,73,80,84,88,99,104,105,
%T A152411 115,120,128,129,143,144,148,153,159,163,168,175,180,185,195,200,201,
%U A152411 208,209,216,224,225,228,240,243,255,260,273,275,280,288,289,303,304,308,319,320
%N A152411 Nonnegative integers representable as m^2 - n^4 for positive integers m,n.
%C A152411 Nonnegative integers representable as the product u*v with (u-v)/2 being a positive square.
%H A152411 Robert Israel, <a href="/A152411/b152411.txt">Table of n, a(n) for n = 1..10000</a>
%p A152411 filter:= proc(x) local d,u;
%p A152411   d:= select(t -> t^2 > x, numtheory:-divisors(x));
%p A152411   for u in d do if issqr((u-x/u)/2) then return true fi od;
%p A152411   false
%p A152411 end proc:
%p A152411 filter(0):= true:
%p A152411 select(filter, [$0..1000]); # _Robert Israel_, Nov 06 2017
%t A152411 filterQ[x_] := Catch[With[{d = Select[Divisors[x], #^2 > x&]}, Do[If[IntegerQ[Sqrt[(u-x/u)/2]], Throw[True]], {u, d}]; Throw[False]]];
%t A152411 filterQ[0] = True;
%t A152411 Select[Range[0, 1000], filterQ] (* _Jean-François Alcover_, Jul 24 2020, after _Robert Israel_ *)
%o A152411 (PARI) for(k=1,1000, fordiv(k,d, if(d*d>=k,break); if( issquare((k\d - d)/2), print1(k,", "); break) ) )
%Y A152411 Cf. A087286, A165289, A152412.
%K A152411 nonn
%O A152411 1,2
%A A152411 _N. J. A. Sloane_, Oct 24 2009, based on email from _Joerg Arndt_, Oct 10 2009
%E A152411 Edited and extended by _Max Alekseyev_, Feb 06 2010