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

1,3

Comments

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

Links

Table of n, a(n) for n=1..105.

Formula

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

Example

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;

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

Crossrefs

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

Sequence in context: A081355 A223708 A060778 * A343856 A053874 A170906

Adjacent sequences: A096489 A096490 A096491 * A096493 A096494 A096495

Keyword

nonn

Author

Labos Elemer, Jun 29 2004

Status

approved