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%I #21 Nov 10 2021 07:07:11
%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 Number of distinct primes in the periodic part of the continued fraction for sqrt(prime(n)).
%H Amiram Eldar, <a href="/A096496/b096496.txt">Table of n, a(n) for n = 1..10000</a>
%e 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.
%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, A096492, A096493, A096494, A096495.
%K nonn
%O 1,8
%A _Labos Elemer_, Jun 29 2004