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Number of distinct terms in continued fraction period of square root of n.
4

%I #10 Nov 10 2021 07:06:59

%S 1,1,2,1,1,2,2,2,1,1,2,2,2,3,2,1,1,2,4,2,3,4,3,2,1,1,2,3,3,2,4,2,3,3,

%T 2,1,1,2,2,2,2,2,4,3,3,5,3,2,1,1,2,4,3,4,2,2,3,2,4,3,5,3,2,1,1,2,5,2,

%U 4,3,4,2,3,2,2,5,4,3,3,2,1,1,2,2,3,4,2,3,3,2,3,4,4,6,3,3,3,3,2,1,1,2,5,2,2

%N Number of distinct terms in continued fraction period of square root of n.

%C Essentially the same as A028832. - _Amiram Eldar_, Nov 10 2021

%F a(n) = 1 if n is a square and a(n) = A028832(n) otherwise. - _Amiram Eldar_, Nov 10 2021

%e n=127: the period={3,1,2,2,7,11,7,2,2,1,3,22},distinct-terms={1,2,3,7,11,22}, so a[127]=6;

%t {tc=Table[0, {m}], u=1}; Do[s=Length[Union[Last[ContinuedFraction[n^(1/2)]]]]; tc[[u]]=s;u=u+1, {n, 1, m}], tc

%Y Cf. A003285, A013646, A028832, A096491, A096493.

%K nonn

%O 1,3

%A _Labos Elemer_, Jun 29 2004