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

720, 5040, 5760, 10080, 20160, 22176, 28800, 56160, 60480, 100800, 126720, 134640, 151200, 187200, 248976, 262080, 282240, 332640, 428400, 443520, 463680, 665280, 677376, 734400, 763776, 887040, 1108800, 1149120, 1190160, 1235520, 1497600, 1685376, 1718640

Offset: 1

Author

Michel Marcus, Oct 30 2012

Keywords

• nonn

Comments

All terms are multiples of 144. - Zak Seidov, Nov 27 2013

Examples

			720 = 27^2 - 3^2 = 28^2 - 8^2 = 29^2 - 11^2.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 1..1000
• E. J. Barbeau, Numbers differing from consecutive squares by squares, Canad. Math. Bull. 28(1985), pp. 337-342.

Crossrefs

Cf. A218485, A218486, A218488.

Programs

Mathematica

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 *)

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, ", ")););}