|
| |
|
|
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
|
| |
|
|
