A152411 - OEIS

%I #15 Jul 24 2020 15:58:47

%S 0,3,8,9,15,19,20,24,33,35,40,48,51,63,65,68,73,80,84,88,99,104,105,

%T 115,120,128,129,143,144,148,153,159,163,168,175,180,185,195,200,201,

%U 208,209,216,224,225,228,240,243,255,260,273,275,280,288,289,303,304,308,319,320

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

%C Nonnegative integers representable as the product u*v with (u-v)/2 being a positive square.

%H Robert Israel, <a href="/A152411/b152411.txt">Table of n, a(n) for n = 1..10000</a>

%p filter:= proc(x) local d,u;

%p   d:= select(t -> t^2 > x, numtheory:-divisors(x));

%p   for u in d do if issqr((u-x/u)/2) then return true fi od;

%p   false

%p end proc:

%p filter(0):= true:

%p select(filter, [$0..1000]); # _Robert Israel_, Nov 06 2017

%t 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 filterQ[0] = True;

%t Select[Range[0, 1000], filterQ] (* _Jean-François Alcover_, Jul 24 2020, after _Robert Israel_ *)

%o (PARI) for(k=1,1000, fordiv(k,d, if(d*d>=k,break); if( issquare((k\d - d)/2), print1(k,", "); break) ) )

%Y Cf. A087286, A165289, A152412.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Oct 24 2009, based on email from _Joerg Arndt_, Oct 10 2009

%E Edited and extended by _Max Alekseyev_, Feb 06 2010