A096496 Number of distinct primes in the periodic part of the continued fraction for sqrt(prime(n)).

1, 1, 0, 0, 1, 0, 0, 2, 1, 1, 2, 0, 1, 2, 1, 1, 2, 2, 3, 2, 1, 1, 0, 2, 1, 0, 1, 1, 2, 1, 4, 2, 1, 4, 2, 4, 3, 4, 1, 0, 4, 1, 3, 2, 0, 3, 4, 1, 0, 1, 1, 2, 2, 2, 0, 0, 1, 1, 3, 1, 1, 0, 4, 3, 3, 1, 5, 3, 2, 2, 2, 1, 3, 2, 4, 2, 1, 2, 0, 3, 4, 5, 5, 3, 1, 0, 3, 4, 1, 4, 1, 3, 3, 2, 1, 1, 2, 2, 2, 4, 4, 0, 2, 3, 4

Offset

1,8

Links

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

Example

n=31: prime(31) = 127, and the periodic part of the continued fraction of sqrt(127) is {3,1,2,2,7,11,7,2,2,1,3,22}, so a(31) = 4.

Mathematica

{te=Table[0, {m}], u=1}; Do[s=Count[PrimeQ[Union[Last[ContinuedFraction[f[n]^(1/2)]]]], True]; te[[u]]=s; u=u+1, {n, 1, m}]; te
Count[Union[ContinuedFraction[Sqrt[#]][[2]]], _?PrimeQ]&/@Prime[ Range[ 110]] (* Harvey P. Dale, Apr 27 2016 *)

Crossrefs

Cf. A003285, A054269, A005980, A096491, A096492, A096493, A096494, A096495.

Sequence in context: A173266 A342149 A224326 * A117209 A035192 A229653

Adjacent sequences: A096493 A096494 A096495 * A096497 A096498 A096499

Keyword

nonn

Author

Labos Elemer, Jun 29 2004

Status

approved