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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

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Last modified September 15 04:07 EDT 2019. Contains 327062 sequences. (Running on oeis4.)