%I #3 Mar 30 2012 18:36:38

%S 1,2,3,4,5,6,7,9,10,12,15,17,18,20,21,25,29,30,34,35,40,41,42,45,50,

%T 51,55,58,60,63,65,68,70,84,85,87,99,102,116,119,126,136,145,153,169,

%U 170,174,187,189,198,203,204,221,232,238,239,252,255,261,272,289,290,297

%N Numerators k for which the partial quotients of the k-CF of sqrt(2) are periodic, where a k-CF is defined as the continued fraction representation having k as the constant numerator: x = q_0 + k/(q_1 + k/(q_2 + k/(q_3 +...))).

%C It is well-known that quadratic numbers have periodic partial quotients in simple continued fractions where the numerators are 1; it is unexpected that similar expressions of quadratics do not remain periodic for most constant numerators k>1.

%Y Cf. A087951.

%K nonn

%O 1,2

%A _Paul D. Hanna_, Sep 16 2003