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

1,2

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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}]
psq[n_]:=With[{s=Sqrt[n]}, If[IntegerQ[s], s, Max[ContinuedFraction[s][[2]]]]]; Array[psq, 80] (* Harvey P. Dale, Oct 26 2025 *)

Crossrefs

Cf. A003285, A013646.

Sequence in context: A195051 A377985 A219654 * A217871 A362872 A306390

Adjacent sequences: A096488 A096489 A096490 * A096492 A096493 A096494

Keyword

nonn

Author

Labos Elemer, Jun 29 2004

Extensions

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

Status

approved