A325605 Lower left-hand y-coordinate for 3 X 3 invisible forest with 0 < x < y.

1308, 2000, 2330, 2714, 3128, 2540, 2924, 3080, 3484, 3794, 3730, 4654, 4730, 4234, 4640, 4718, 5300, 5564, 5654, 4928, 5704, 5654, 5718, 4598, 5654, 4640, 5642, 6200, 4640, 5150, 4598, 6094, 5984, 5984, 6408, 6460, 4674, 4794, 6104, 5620

Offset: 1

Author

Benjamin Hutz, May 31 2019

Keywords

• nonn

Comments

These are 3 X 3 rectangles of lattice points not visible along straight lines of sight from the origin. The sequence is ordered by Euclidean distance from (0,0).

Examples

			1308 is a term because (1274, 1308) is the lower left-hand coordinate of a 3 X 3 invisible forest, i.e., gcd(1274+i, 1308+j) > 1 for 0 <= i <= 2 and 0 <= j <= 2.
Other such coordinates are (1884, 2000), (1924, 2330), (1448, 2714), (594, 3128), (2254, 2540), (2364, 2924), (2210, 3080), (1598, 3484), (1000, 3794).
		

Links

• E. Goins, P. Harris, B. Kubik, A. Mbirika, Lattice Point Visibility on Generalized Lines of Sight, arXiv:1710.04554 [math.NT], 2017; Amer. Math. Monthly 125 (2018) 593-601.
• F. Herzog, B. M. Stewart, Patterns of Visible and Nonvisible Lattice Points, Amer. Math. Monthly 78 (1971) 487-496.
• S. Laishram, F. Luca, Rectangles Of Nonvisible Lattice Points, J. Int. Seq. 18 (2015) 15.10.8.

Crossrefs

Cf. A157426, A157427, A157428, A157429.

Cf. A325602, A325603, A325604, A325606, A325607.