|
Search: id:A141247
|
|
|
| A141247 |
|
Minimum number of points visible from a point in a square n X n lattice. |
|
+0
2
|
|
| 1, 4, 6, 10, 14, 22, 26, 38, 46, 58, 66, 86, 94, 118, 130, 146, 162, 194, 206, 241, 257, 282, 302, 346, 362, 401, 426, 462, 486, 542, 558, 609, 641, 690, 722, 770, 794, 861, 899, 950, 982, 1062, 1086, 1157, 1201, 1258, 1302, 1393, 1425, 1501, 1546, 1613
(list; graph; listen)
|
|
|
OFFSET
|
1,2
|
|
|
COMMENT
|
Two points (a,b) and (c,d) are visible to each other when gcd(c-a,d-b)=1. Sequence A141248 gives the number of lattice points that have minimal visibility.
|
|
LINKS
|
T. D. Noe, Table of n, a(n) for n=1..1000
Eric Weisstein, MathWorld: Visible Point
|
|
FORMULA
|
The minimum number of visible points is slightly less than c*n^2, with c = 6/pi^2.
|
|
MATHEMATICA
|
Table[mn=n^2+1; Do[cnt=0; Do[If[GCD[c-a, d-b]<2, cnt++ ], {a, n}, {b, n}]; If[cnt<mn, mn=cnt], {c, n}, {d, n}]; mn, {n, 20}]
|
|
CROSSREFS
|
Cf. A141224.
Sequence in context: A100484 A076924 A103801 this_sequence A049632 A061227 A000066
Adjacent sequences: A141244 A141245 A141246 this_sequence A141248 A141249 A141250
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
T. D. Noe (noe(AT)sspectra.com), Jun 17 2008
|
|
|
Search completed in 0.002 seconds
|
