A096493 Number of distinct primes in continued fraction period of square root of n.

0, 1, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 2, 1, 1, 1, 1, 0, 0, 0, 1, 2, 1, 1, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 2, 1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 0, 0, 2, 1, 2, 0, 0, 0, 0, 0, 3, 0, 1, 1, 2, 1, 1, 0, 0, 2, 2, 0, 1, 0, 0, 0, 0, 0, 0, 1, 1, 1, 2, 1, 1, 1, 0, 3, 1, 1, 1, 0, 0, 0, 0, 0, 1, 1, 0

Offset

1,19

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Example

n=127: the period={3,1,2,2,7,11,7,2,2,1,3,22},
distinct-primes={2,3,7,11}, so a[127]=4;

Mathematica

{te=Table[0, {m}], u=1}; Do[s=Count[PrimeQ[Union[Last[ContinuedFraction[n^(1/2)]]]], True]; te[[u]]=s; u=u+1, {n, 1, m}]; te
dpcf[n_]:=Module[{s=Sqrt[n]}, If[IntegerQ[s], 0, Count[Union[ ContinuedFraction[ s][[2]]], _?PrimeQ]]]; Array[dpcf, 110] (* Harvey P. Dale, Mar 18 2016 *)

Crossrefs

Cf. A003285, A013646, A096491, A096492.

Sequence in context: A244250 A167230 A093658 * A269242 A321759 A076882

Adjacent sequences: A096490 A096491 A096492 * A096494 A096495 A096496

Keyword

nonn

Author

Labos Elemer, Jun 29 2004

Status

approved