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A096495
Number of distinct terms in the periodic part of the continued fraction for sqrt(prime(n)).
3
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
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 *)
KEYWORD
nonn
AUTHOR
Labos Elemer, Jun 29 2004
STATUS
approved