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

1,1

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).

Links

Table of n, a(n) for n=1..40.

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.

Example

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).

Crossrefs

Cf. A157426, A157427, A157428, A157429.

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

Sequence in context: A255025 A126841 A106815 * A281211 A233975 A209853

Adjacent sequences: A325602 A325603 A325604 * A325606 A325607 A325608

Keyword

nonn

Author

Benjamin Hutz, May 31 2019

Status

approved