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 A325603 Lower left-hand y-coordinate for 2 X 2 invisible forest with 0 < x < y. 9
 20, 35, 35, 54, 65, 77, 69, 84, 84, 98, 99, 104, 99, 95, 114, 104, 119, 98, 110, 114, 104, 132, 135, 119, 132, 153, 135, 174, 174, 161, 175, 147, 170, 186, 189, 159, 189, 153, 170, 195, 189, 195, 185, 195, 185, 195, 209, 216, 224, 224 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS These are 2 X 2 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 Benjamin Hutz, Table of n, a(n) for n = 1..1000 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 (14,20), (14,35), (20,35), (44,54), (39,65), (21,77), (45,69), (34,84). PROG def is_nxn(x, y, n): if all([gcd(x+a, y+b) != 1 for a in range(n) for b in range(n)]): return True return False def insert_item(pts, item, index): N = len(pts) if N == 0: return [item] elif N == 1: if item[index] < pts[0][index]: pts.insert(0, item) else: pts.append(item) return pts else: #binary insertion left = 1 right = N mid = ((left + right)/2).floor() if item[index] < pts[mid][index]: # item goes into first half return insert_item(pts[:mid], item, index) + pts[mid:N] else: # item goes into second half return pts[:mid] + insert_item(pts[mid:N], item, index) B=1200 L=[] for x in range(1, B): for y in range(x+1, B): if is_nxn(x, y, n=2): G=[x, y, x^2+y^2] L=insert_item(L, G, 2) CROSSREFS Cf. A157426, A157427, A157428, A157429, A325602, A325604, A325605, A325606, A325607. Sequence in context: A068476 A003895 A157426 * A024747 A328051 A081962 Adjacent sequences: A325600 A325601 A325602 * A325604 A325605 A325606 KEYWORD nonn AUTHOR Benjamin Hutz, May 10 2019 STATUS approved

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Last modified January 30 02:40 EST 2023. Contains 359939 sequences. (Running on oeis4.)