A096491 a(n) = sqrt(n) of n if n is a perfect square, otherwise a(n) = largest term in period of continued fraction expansion of square root of n.

1, 2, 2, 2, 4, 4, 4, 4, 3, 6, 6, 6, 6, 6, 6, 4, 8, 8, 8, 8, 8, 8, 8, 8, 5, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 6, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 7, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 14, 8, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16

Offset: 1

Author

Labos Elemer, Jun 29 2004

Keywords

• nonn

Examples

			For n=127: the period={3,1,2,2,7,11,7,2,2,1,3,22}, max=a(127)=22.
		

Crossrefs

Cf. A003285, A013646.

Programs

Maple

A096491 := proc(n)
if issqr(n) then
sqrt(n) ;
else
numtheory[cfrac](sqrt(n),'periodic','quotients') ;
%[2] ;
max(op(%)) ;
end if;
end proc:
# R. J. Mathar, Mar 18 2010

Mathematica

u=1;Do[s=Max[Last[ContinuedFraction[n^(1/2)]]];tc[[u]]=s;u=u+1, {n, 1, m}]

Extensions

Definition revised by N. J. A. Sloane, Mar 18 2010