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A260549 Primitive values n such that the square with opposite corners (0,0) and (n,n) contains a point (x,y) with integer coordinates, with 0 < x,y < n, at an integer distance from three of the four corners.

%I A260549 #9 Jul 31 2015 04:12:42
%S A260549 52,195,700,740,867,996,1443,2145,3364,6015,6240,7800,8400,9165,9375,
%T A260549 10879,10952,11184,11352,11484,11492,11997,12675,13156,14355,14739,
%U A260549 20280,20415,20625,20988,21125,21320,21853,22472,23069,26180,26588,27189,28168,30195
%N A260549 Primitive values n such that the square with opposite corners (0,0) and (n,n) contains a point (x,y) with integer coordinates, with 0 < x,y < n, at an integer distance from three of the four corners.
%C A260549 Primitiveness condition prescribes that, if n is in the sequence because of the interior point (x, y), then GCD(x, y, n) = 1.
%C A260549 Some values admit more than one qualifying interior point. For example, for n = 21125 we have both (4416, 3737) and (8357, 7524).
%C A260549 This sequence is a superset of A215365, which only contains even values.
%H A260549 Giovanni Resta, <a href="/A260549/b260549.txt">Table of n, a(n) for n = 1..75</a> (terms < 130000)
%e A260549 700 is in the sequence because the point (304,297) is at distance 425 from (0,0), 495 from (700,0) and 565 from (700,700) and GCD(700,304,297) = 1.
%Y A260549 Cf. A215365.
%K A260549 nonn
%O A260549 1,1
%A A260549 _Mark Underwood_ and _Giovanni Resta_, Jul 29 2015