

A096495


Number of distinct terms in repeating part of continued fraction of square root of nth prime.


2



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
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OFFSET

1,2


LINKS

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


EXAMPLE

n=31: prime(31) = 127, and the repeating 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, A054269, A005980, A096491A096496.
Sequence in context: A241318 A276064 A054992 * A276062 A324386 A233390
Adjacent sequences: A096492 A096493 A096494 * A096496 A096497 A096498


KEYWORD

cofr,nonn


AUTHOR

Labos Elemer, Jun 29 2004


STATUS

approved



