A216467 -id:A216467 - cp's OEIS frontend

A178793 These are the y coordinates of isolated visible lattice points in the plane.

55, 175, 551, 575, 589, 609, 679, 741, 741, 791, 799, 805, 875, 945, 987, 987, 995, 1035, 1065, 1105, 1105, 1159, 1209, 1275, 1309, 1309, 1309, 1407, 1421, 1463, 1463, 1463, 1495, 1495, 1551, 1581, 1581, 1611, 1625, 1639, 1651, 1665, 1665, 1665, 1695

Offset: 1

Gregg Whisler, Jun 15 2010

nonn

From Gregg Whisler, Jun 21 2010: (Start)
a(n) is also A157428 + 1. [Charles R Greathouse IV points out that this is false, since (1308, 1274) is in (A157428, A157429) but not in (A178793, A178794). Oct 17 2012]
An isolated lattice point is surrounded (in a Moore neighborhood of r=1) in the Z^2 lattice of points by 8 points that are not visible from the origin. (End)

Eric W. Weisstein, Visible Point

Cf. A157428, A157429, A178794 (corresponding x coordinates), A216467.

Table[Replace[Select[First/@Position[Partition[CoprimeQ[n,Range[n]],3,1],{False,True,False},{1}]+1, Outer[CoprimeQ, n+ {-1,1},#1+{-1,0,1}]=={{False,False,False},{False,False,False}}&],{{}-> Sequence[], list_:>Sequence@@ ({#1,n}&)/@list}],{n,2000}][[All, 2]] (* Eric Rowland *)

More terms (until the corresponding first x coordinate (21) repeats) from Gregg Whisler, Jun 21 2010

A178794 These are the x coordinates of the isolated visible lattice points in the plane.

Original entry on oeis.org

21, 99, 115, 369, 495, 475, 195, 259, 265, 225, 375, 741, 741, 649, 323, 377, 399, 1001, 1001, 441, 987, 609, 755, 1001, 545, 645, 1035, 407, 1275, 153, 645, 1275, 51, 1221, 485, 35, 805, 715, 441, 595, 1015, 221, 1001, 1183, 371, 391, 575, 519, 645, 1065

Offset: 1

Gregg Whisler, Jun 15 2010

nonn

An isolated lattice point is surrounded (in a Moore neighborhood) by 8 points that are not visible from the origin. I have also submitted the corresponding sequence of denominators.
From Gregg Whisler, Jun 21 2010: (Start)
a(n) is also A157429 + 1.
These are also the x coordinates of the isolated visible lattice points in Z^2. (End)

Eric W. Weisstein, MathWorld: Visible Point

Cf. A178793 (corresponding y coordinates), A157428, A157429, A216467.

Table[Replace[Select[First/@Position[Partition[CoprimeQ[n,Range[n]],3,1],{False,True,False},{1}]+1, Outer[CoprimeQ, n+ {-1,1},#1+{-1,0,1}]=={{False,False,False},{False,False,False}}&],{{}-> Sequence[], list_:>Sequence@@ ({#1,n}&)/@list}],{n,2000}][[All, 1]] (* Eric Rowland *)

More terms (until the initial 21 repeats) from Gregg Whisler, Jun 21 2010

cp's OEIS Frontend

A178793 These are the y coordinates of isolated visible lattice points in the plane.

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