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A218487 Positive numbers differing from next 3 greater squares by squares. 3

%I

%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

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Last modified December 8 20:37 EST 2021. Contains 349596 sequences. (Running on oeis4.)