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A096496 Number of distinct primes in the periodic part of the continued fraction for sqrt(prime(n)). 3
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 3 17:00 EST 2023. Contains 360044 sequences. (Running on oeis4.)