A260549 - OEIS

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.

52, 195, 700, 740, 867, 996, 1443, 2145, 3364, 6015, 6240, 7800, 8400, 9165, 9375, 10879, 10952, 11184, 11352, 11484, 11492, 11997, 12675, 13156, 14355, 14739, 20280, 20415, 20625, 20988, 21125, 21320, 21853, 22472, 23069, 26180, 26588, 27189, 28168, 30195

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OFFSET

1,1

COMMENTS

Primitiveness condition prescribes that, if n is in the sequence because of the interior point (x, y), then GCD(x, y, n) = 1.

Some values admit more than one qualifying interior point. For example, for n = 21125 we have both (4416, 3737) and (8357, 7524).

This sequence is a superset of A215365, which only contains even values.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..75 (terms < 130000)

EXAMPLE

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.

CROSSREFS