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

1,1

Comments

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

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.

Example

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

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 *)

Prog

(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, ", ")); ); }

Crossrefs

Cf. A218485, A218486, A218488.

Sequence in context: A233787 A280920 A187290 * A053625 A052793 A179728

Adjacent sequences: A218484 A218485 A218486 * A218488 A218489 A218490

Keyword

nonn

Author

Michel Marcus, Oct 30 2012

Status

approved