A096495 Number of distinct terms in the periodic part of the continued fraction for sqrt(prime(n)).

1, 2, 1, 2, 2, 2, 1, 4, 3, 3, 4, 1, 2, 4, 3, 3, 4, 5, 5, 4, 3, 3, 2, 3, 3, 1, 5, 4, 6, 3, 6, 4, 3, 6, 5, 7, 5, 6, 3, 3, 6, 6, 6, 5, 1, 7, 8, 3, 2, 3, 3, 6, 5, 5, 1, 4, 2, 7, 7, 5, 6, 3, 6, 6, 6, 5, 8, 6, 5, 4, 4, 3, 7, 3, 9, 4, 3, 7, 1, 6, 6, 8, 7, 6, 3, 2, 5, 7, 5, 9, 4, 6, 9, 8, 4, 4, 6, 6, 8, 9, 8, 2, 4, 6, 10

Offset

1,2

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Formula

a(n) = A028832(A000040(n)). - Amiram Eldar, Nov 10 2021

Example

n = 31: prime(31) = 127, and the periodic part is {3,1,2,2,7,11,7,2,2,1,3,22}, so a(31) = 6.

Mathematica

{te=Table[0, {m}], u=1}; Do[s=Length[Union[Last[ContinuedFraction[Prime[n]^(1/2)]]]]; te[[u]]=s; u=u+1, {n, 1, m}]; te
Table[Length[Union[ContinuedFraction[Sqrt[Prime[n]]][[2]]]], {n, 110}] (* Harvey P. Dale, Jun 22 2017 *)

Crossrefs

Cf. A003285, A028832, A054269, A005980, A096491, A096492, A096493, A096494, A096496.

Sequence in context: A241318 A276064 A054992 * A276062 A324386 A233390

Adjacent sequences: A096492 A096493 A096494 * A096496 A096497 A096498

Keyword

nonn

Author

Labos Elemer, Jun 29 2004

Status

approved