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A059800 Smallest prime p such that the quotient-cycle length in continued fraction expansion of sqrt(p) is n: smallest prime p(m) for which A054269(m)=n.

%I A059800 #9 Jul 07 2018 19:19:34
%S A059800 2,3,41,7,13,19,73,31,113,43,61,103,193,179,109,191,157,139,337,151,
%T A059800 181,491,853,271,457,211,1109,487,821,379,601,463,613,331,1061,1439,
%U A059800 421,619,541,1399,1117,571,1153,823,1249,739,1069,631,1021,1051,1201
%N A059800 Smallest prime p such that the quotient-cycle length in continued fraction expansion of sqrt(p) is n: smallest prime p(m) for which A054269(m)=n.
%H A059800 T. D. Noe, <a href="/A059800/b059800.txt">Table of n, a(n) for n = 1..2000</a>
%F A059800 a(n) = Min{p|A054269(sequence number of p)=n; p is prime}.
%e A059800 The quotient-cycle length L=9=A054269(m) first appears for p(30)=113, so a(9)=113 namely, at first A054269(30)=9; a(A054269(30)) = p(30) = 113 = a(9). The quotient cycle with L=16 first emerges for sqrt(191) and it is: cfrac(sqrt(191), 'periodic', 'quotients')= [[13],[1,4,1,1,3,2,2,13,2 2,3,1,1,4,1,26]].
%Y A059800 Cf. A054269.
%Y A059800 Cf. A013646, A130272
%K A059800 nonn
%O A059800 1,1
%A A059800 _Labos Elemer_, Feb 23 2001