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A288184 Least odd number k such that the continued fraction for sqrt(k) has period n.

%I A288184 #15 Feb 16 2025 08:33:47
%S A288184 5,3,41,7,13,19,73,31,113,43,61,103,193,179,109,133,157,139,337,151,
%T A288184 181,253,853,271,457,211,949,487,821,379,601,463,613,331,1061,1177,
%U A288184 421,619,541,589,1117,571,1153,823,1249,739,1069,631,1021,1051,1201,751
%N A288184 Least odd number k such that the continued fraction for sqrt(k) has period n.
%H A288184 Chai Wah Wu, <a href="/A288184/b288184.txt">Table of n, a(n) for n = 1..10000</a>
%H A288184 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PeriodicContinuedFraction.html">Periodic Continued Fraction</a>
%F A288184 A003285(a(n)) = n, A000035(a(n)) = 1.
%e A288184 a(2) = 3, sqrt(3) = 1 + 1/(1 + 1/(2 + 1/(1 + 1/(2 + 1/...)))), period 2: [1, 2].
%o A288184 (Python)
%o A288184 from sympy import continued_fraction_periodic
%o A288184 def A288184(n):
%o A288184     d = 1
%o A288184     while True:
%o A288184         s = continued_fraction_periodic(0,1,d)[-1]
%o A288184         if isinstance(s, list) and len(s) == n:
%o A288184             return d
%o A288184         d += 2 # _Chai Wah Wu_, Jun 07 2017
%Y A288184 Cf. A000035, A003285, A010337-A010339, A013642-A013644, A013646, A013943, A020347-A020439, A059800, A062769, A097853, A288185.
%K A288184 nonn
%O A288184 1,1
%A A288184 _Ilya Gutkovskiy_, Jun 06 2017