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

Author

Gregory V. Richardson, Jan 05 2014

Keywords

• nonn
• hard
• more

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

Examples

			See picture in Links.
		

Links

• New Scientist Magazine, Enigma #1686, 22 February 2012.
• Giovanni Resta, Illustration for a(2) and a(3)
• Gregory V. Richardson, QuickBasic 64 program

Programs

QuickBASIC

' See Links.