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A325602
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Lower left-hand x-coordinate for 2 X 2 invisible forest with 0 < x < y.
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9
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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
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history;
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internal format)
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OFFSET
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1,1
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COMMENTS
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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).
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LINKS
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EXAMPLE
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(14,20), (14,35), (20,35), (44,54), (39,65), (21,77), (45,69), (34,84), ...
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PROG
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(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)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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