login
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.
7
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
1,2
EXAMPLE
For n=127: the period={3,1,2,2,7,11,7,2,2,1,3,22}, max=a(127)=22.
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}]
CROSSREFS
Sequence in context: A087627 A195051 A219654 * A217871 A362872 A306390
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 29 2004
EXTENSIONS
Definition revised by N. J. A. Sloane, Mar 18 2010
STATUS
approved