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 A096496 Count of distinct primes in period of continued fraction of square root of n-th prime. 2

%I

%S 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,

%T 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,

%U 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

%N Count of distinct primes in period of continued fraction of square root of n-th prime.

%e n=31,p[31]=127: the period={3,1,2,2,7,11,7,2,2,1,3,22}, so a[31]=4;

%t {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

%t Count[Union[ContinuedFraction[Sqrt[#]][[2]]],_?PrimeQ]&/@Prime[ Range[ 110]] (* _Harvey P. Dale_, Apr 27 2016 *)

%Y Cf. A003285, A054269, A005980, A096491-A096495.

%K cofr,nonn

%O 1,8

%A _Labos Elemer_, Jun 29 2004

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