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

0, 3, 8, 9, 15, 19, 20, 24, 33, 35, 40, 48, 51, 63, 65, 68, 73, 80, 84, 88, 99, 104, 105, 115, 120, 128, 129, 143, 144, 148, 153, 159, 163, 168, 175, 180, 185, 195, 200, 201, 208, 209, 216, 224, 225, 228, 240, 243, 255, 260, 273, 275, 280, 288, 289, 303, 304, 308, 319, 320

Offset

1,2

Comments

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

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

filter:= proc(x) local d, u;
  d:= select(t -> t^2 > x, numtheory:-divisors(x));
  for u in d do if issqr((u-x/u)/2) then return true fi od;
  false
end proc:
filter(0):= true:
select(filter, [$0..1000]); # Robert Israel, Nov 06 2017

Mathematica

filterQ[x_] := Catch[With[{d = Select[Divisors[x], #^2 > x&]}, Do[If[IntegerQ[Sqrt[(u-x/u)/2]], Throw[True]], {u, d}]; Throw[False]]];
filterQ[0] = True;
Select[Range[0, 1000], filterQ] (* Jean-François Alcover, Jul 24 2020, after Robert Israel *)

Prog

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

Crossrefs

Cf. A087286, A165289, A152412.

Sequence in context: A287579 A289142 A101065 * A080517 A264898 A248194

Adjacent sequences: A152408 A152409 A152410 * A152412 A152413 A152414

Keyword

nonn

Author

N. J. A. Sloane, Oct 24 2009, based on email from Joerg Arndt, Oct 10 2009

Extensions

Edited and extended by Max Alekseyev, Feb 06 2010

Status

approved