A096492 Number of distinct terms in continued fraction period of square root of n.

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, 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, 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

Offset: 1

Author

Labos Elemer, Jun 29 2004

Keywords

• nonn

Comments

Essentially the same as A028832. - Amiram Eldar, Nov 10 2021

Examples

			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;
		

Crossrefs

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

Programs

Mathematica

{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

Formula

a(n) = 1 if n is a square and a(n) = A028832(n) otherwise. - Amiram Eldar, Nov 10 2021