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

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

Cf. A215365.

Sequence in context: A166390 A161478 A288919 * A211564 A346825 A346858

Adjacent sequences: A260546 A260547 A260548 * A260550 A260551 A260552

Keyword

nonn

Author

Mark Underwood and Giovanni Resta, Jul 29 2015

Status

approved