A097853 - OEIS

%I #13 Jan 09 2025 09:22:08

%S 1,1,2,1,1,2,4,2,1,1,2,2,5,4,2,1,1,2,6,2,6,6,4,2,1,1,2,4,5,2,8,4,4,4,

%T 2,1,1,2,2,2,3,2,10,8,6,12,4,2,1,1,2,6,5,6,4,2,6,7,6,4,11,4,2,1,1,2,

%U 10,2,8,6,8,2,7,5,4,12,6,4,4,2,1,1,2,2,5,10,2,6,5,2,8,8,10,16,4,4,11,4,2,1,1,2,12

%N Period of continued fraction for square root of n (or 1 if n is a square).

%e 1 is a square. 2 has continued fraction [1;2,2,2...], 3 has [1;1,2,1,2,1,2...]. - _Georg Fischer_, Jun 14 2019

%p a:= n-> `if`(issqr(n), 1, nops(numtheory[cfrac](

%p          sqrt(n), 'periodic', 'quotients')[2])):

%p seq(a(n), n=1..120);  # _Alois P. Heinz_, Jun 14 2019

%t a[n_] := If[IntegerQ[Sqrt[n]], 1, Length[ContinuedFraction[Sqrt[n]][[2]]]];

%t Table[a[n], {n, 1, 103}] (* _Jean-François Alcover_, Jan 09 2025 *)

%Y See A003285, which is the main entry for this sequence.

%K nonn,easy

%O 1,3

%A _N. J. A. Sloane_, Sep 01 2004