A362669 Integer inradii for which there exists an isosceles triangle with integer sides (a, b, b) where a < b.

10, 20, 21, 24, 30, 36, 40, 42, 48, 50, 55, 60, 63, 70, 72, 78, 80, 84, 90, 96, 100, 105, 108, 110, 112, 120, 126, 130, 136, 140, 144, 147, 150, 156, 160, 165, 168, 170, 171, 180, 189, 190, 192, 195, 200, 210, 216, 220, 224, 230, 231, 234, 240, 250, 252, 253, 260, 264, 270, 272, 273, 275

Offset

1,1

Comments

The inradius for isosceles triangle (a, b, b) is r = (a/2)*sqrt((2*b-a)/(2*b+a)).

If m is a term, so is k*m with k > 1; hence, A008592 \ {0} is a subsequence.

Links

Table of n, a(n) for n=1..62.

Eric Weisstein's World of Mathematics, Incircle.

Eric Weisstein's World of Mathematics, Isosceles Triangle.

Example

The smallest inradius, r = 10, corresponds to isosceles triangle (30, 39, 39).
The third inradius, r = 21, corresponds to isosceles triangle (56, 100, 100).
r = 60 is the first inradius for which there exist two such isosceles triangles: (168, 259, 259) and (180, 234, 234).

Mathematica

Select[Range[300], Length @ Reduce[#^2 == a^2*(2*b - a)/(4*(2*b + a)) && 0 < a < b, {a, b}, Integers] > 0 &] (* Amiram Eldar, May 05 2023 *)

Crossrefs

Cf. A008592, A070204, A120062, A120570, A362670 (similar but with (a,a,c)).

Sequence in context: A040090 A183195 A098176 * A132782 A267759 A297270

Adjacent sequences: A362666 A362667 A362668 * A362670 A362671 A362672

Keyword

nonn

Author

Bernard Schott, Apr 29 2023

Status

approved