A235230 Integer radii of circles tiled by square tiles such that the ratio of uncut tiles to cut tiles is an integer and four square tiles meet at the center of the circle.

1, 6, 15, 364, 585, 5052, 9573, 191714, 13682428

Offset

1,2

Comments

It is my conjecture that there are an infinite number of solutions and that they occur by chance, accounting for the widening gaps between valid answers as the number of digits for the sums of tiles increases.

The inspiration for this problem came from Enigma #1686 of the New Scientist Magazine.

The values involved are the following {a(n), #uncut, cut, ratio} : {1, 0, 4, 0}, {6, 88, 44, 2}, {15, 648, 108, 6}, {364, 414700, 2900, 143}, {585, 1072764, 4644, 231}, {5052, 80161536, 40404, 1984}, {9573, 287864220, 76580, 3759},{191714, 115466138200, 1533700, 75286}, {13682428, 588133849050724, 109459412, 5373077}. No further terms up to 15*10^6. - Giovanni Resta, Jan 06 2014

Links

Table of n, a(n) for n=1..9.

New Scientist Magazine, Enigma #1686, 22 February 2012.

Giovanni Resta, Illustration for a(2) and a(3)

Gregory V. Richardson, QuickBasic 64 program

Example

See picture in Links.

Prog

See Links.

Crossrefs

Sequence in context: A003155 A335578 A199095 * A024081 A145558 A145612

Adjacent sequences: A235227 A235228 A235229 * A235231 A235232 A235233

Keyword

nonn,hard,more

Author

Gregory V. Richardson, Jan 05 2014

Status

approved