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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
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
New Scientist Magazine, Enigma #1686, 22 February 2012.
Gregory V. Richardson, QuickBasic 64 program
EXAMPLE
See picture in Links.
PROG
(QuickBASIC) ' See Links.
CROSSREFS
Sequence in context: A003155 A335578 A199095 * A024081 A145558 A145612
KEYWORD
nonn,hard,more
AUTHOR
STATUS
approved