A083869 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.

1, 3, 55, 43631, 99515655135, 4723258824886629604131775, 589359179694820074404152604620573424809709490316113791, 13331474848620898858862175943355927686887898121894707763190978243005066121710225087713374054319814910927464555589375

Offset: 1

Author

Benoit Cloitre, Jun 18 2003

Keywords

• nonn

Examples

			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.
		

Crossrefs

Cf. A166994. [Paul D. Hanna, Nov 18 2009]

Formula

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

Equals main diagonal of triangle A166994. [Paul D. Hanna, Nov 18 2009]