

A272268


Records in A001481 that are more than twice the previous record.


1



1, 4, 9, 20, 41, 85, 173, 349, 701, 1405, 2813, 5629, 11261, 22525, 45053, 90113, 180232, 360466, 720937, 1441877, 2883761, 5767525, 11535053, 23070112, 46140228, 92280457, 184560921, 369121849, 738243700, 1476487402, 2952974809, 5905949620, 11811899241
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

This list can be seen as the r^2 (square of the radius r) of the homocentric circles that are centered at the origin and pass through at least 4 lattice points, the innermost circle being the unit circle.
If we start with the unit circle (x^2 + y^2 = 1), the smallest circle that pass through at least four lattice points would be x^2 + y^2 = 4 with (2,0), (0,2), (2,0), (0,2). Similarly next circle would be x^2 + y^2 = 9 passing through (3,0), (0,3), (3,0), (0,3), and the next x^2 + y^2 = 20 passing through (2,4), (4,2), (2,4), (4,2), (2,4), (4,2), (2,4), (4,2), etc.
It is also worth mentioning that a square can be drawn with vertexes on the lattice points of a circle and the sides of that square wouldn't touch the smaller circle.


LINKS

Table of n, a(n) for n=1..33.
M. Sinan Kul, PARI/GP code


MATHEMATICA

NestList[SelectFirst[Range[2 # + 1, 5 #], SquaresR[2, #] > 0 &] &, 1, 25] (* Michael De Vlieger, Apr 25 2016, Version 10 *)


CROSSREFS

Cf. A001481.
Sequence in context: A117074 A072934 A084639 * A284736 A051136 A156321
Adjacent sequences: A272265 A272266 A272267 * A272269 A272270 A272271


KEYWORD

nonn


AUTHOR

M. Sinan Kul, Apr 24 2016


STATUS

approved



