OFFSET
1,1
COMMENTS
The inradius for isosceles triangle (a, a, c) is r = (c/2)*sqrt((2*a-c)/(2*a+c)).
If m is a term, so is k*m with k > 1.
As r = 3 and r = 4 are terms, A008585 and A008586 are respective subsequences; the only terms < 100 that are not multiples of 3 or 4 are 35 and 70, the next one is r = 154 = 2*7*11 for triple (765, 765, 1386).
By the triangle inequality, a+1 <= c <= 2*a-1.
Differs from A059267. Examples: 154 is not in A059267 but in this sequence at radius r=154 with side lengths c=1386 and a=765. 442 is not in A059267 but in this sequences with r=442, c=6630, a=3435. - R. J. Mathar, Jun 26 2023
LINKS
R. J. Mathar, Solution strategy and Maple program
Eric Weisstein's World of Mathematics, Incircle.
Eric Weisstein's World of Mathematics, Isosceles Triangle.
EXAMPLE
The smallest inradius r = 3 corresponds to isosceles triangle (10, 10, 12).
The second inradius r = 4 corresponds to isosceles triangle (15, 15, 24).
r = 15 is the first inradius for which there exist two such isosceles triangles: (50, 50, 60) and (68, 68, 120).
r = 35 is the smallest inradius that is not multiple of 3 or of 4, this inradius corresponds to isosceles triangle (222, 222, 420).
CROSSREFS
KEYWORD
nonn
AUTHOR
Bernard Schott, May 05 2023
STATUS
approved