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 A325602 Lower left-hand x-coordinate for 2 X 2 invisible forest with 0 < x < y. 9
 14, 14, 20, 44, 39, 21, 45, 34, 50, 21, 44, 39, 54, 75, 45, 65, 34, 77, 74, 69, 90, 56, 50, 84, 76, 33, 84, 14, 20, 69, 55, 111, 75, 33, 14, 105, 35, 119, 95, 20, 56, 35, 74, 90, 110, 104, 76, 62, 20, 35 (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 (Python) 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. Cf. A325603, A325604, A325605, A325606, A325607. Sequence in context: A291510 A186128 A105707 * A157427 A003905 A205702 Adjacent sequences: A325599 A325600 A325601 * A325603 A325604 A325605 KEYWORD nonn AUTHOR Benjamin Hutz, May 10 2019 STATUS approved

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Last modified January 28 10:39 EST 2023. Contains 359859 sequences. (Running on oeis4.)