A083869 - OEIS

%I #14 Mar 23 2016 11:26:33

%S 1,3,55,43631,99515655135,4723258824886629604131775,

%T 589359179694820074404152604620573424809709490316113791,

%U 13331474848620898858862175943355927686887898121894707763190978243005066121710225087713374054319814910927464555589375

%N a(1)=1 then a(n) is the least k>=1 such that the nested radical sqrt(a(1)^2+sqrt(a(2)^2+sqrt(a(3)^2+(....+sqrt(a(n)^2)))...) is an integer.

%F n = sqrt(a(1)^2+sqrt(a(2)^2+sqrt(a(3)^2+(....+sqrt(a(n)^2)))...).

%F Equals main diagonal of triangle A166994. [_Paul D. Hanna_, Nov 18 2009]

%e k=55 is the least integer such that sqrt(1^2+sqrt(3^2+sqrt(k^2)))=3 is an integer hence a(3)=55.

%Y Cf. A166994. [_Paul D. Hanna_, Nov 18 2009]

%K nonn

%O 1,2

%A _Benoit Cloitre_, Jun 18 2003