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%I #17 Apr 18 2021 14:40:01
%S 720,5040,5760,10080,20160,22176,28800,56160,60480,100800,126720,
%T 134640,151200,187200,248976,262080,282240,332640,428400,443520,
%U 463680,665280,677376,734400,763776,887040,1108800,1149120,1190160,1235520,1497600,1685376,1718640
%N Positive numbers differing from next 3 greater squares by squares.
%C All terms are multiples of 144. - _Zak Seidov_, Nov 27 2013
%H Donovan Johnson, <a href="/A218487/b218487.txt">Table of n, a(n) for n = 1..1000</a>
%H E. J. Barbeau, <a href="http://dx.doi.org/10.4153/CMB-1985-040-9">Numbers differing from consecutive squares by squares</a>, Canad. Math. Bull. 28(1985), pp. 337-342.
%e 720 = 27^2 - 3^2 = 28^2 - 8^2 = 29^2 - 11^2.
%t Select[Range[172*10^4],AllTrue[Sqrt[(Floor[Sqrt[#]]+{1,2,3})^2-#],IntegerQ]&] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Apr 18 2021 *)
%o (PARI) sq3(n) = {for (i=1, n, a = sqrtint(i) + 1; if (issquare(a^2-i) && issquare((a+1)^2-i) && issquare((a+2)^2-i), print1(i, ", ")););}
%Y Cf. A218485, A218486, A218488.
%K nonn
%O 1,1
%A _Michel Marcus_, Oct 30 2012