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%I #19 Apr 24 2022 06:35:52
%S 2,4,0,8,10,16,22,32,44,64,90,128,180,256,362,512,724,1024,1448,2048,
%T 2896,4096,5792,8192,11584,16384,23170,32768,46340,65536,92680,131072,
%U 185362,262144,370726,524288,741454,1048576,1482910,2097152,2965820,4194304,5931640
%N Largest term in periodic part of continued fraction expansion of square root of 2^n + 1 or 0 if 2^n + 1 is a square.
%C a(n) = 0 iff n = 3, as a consequence of Catalan's conjecture or Mihăilescu's theorem. - _Bernard Schott_, Apr 22 2022
%H Chai Wah Wu, <a href="/A077624/b077624.txt">Table of n, a(n) for n = 1..78</a>
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Catalan's_conjecture">Catalan's conjecture</a>.
%t Table[Max[Last[ContinuedFraction[Sqrt[1+2^u]]]], {u, 1, 32}]
%Y Cf. A077625-A077635.
%K nonn
%O 1,1
%A _Labos Elemer_, Nov 13 2002
%E Definition clarified, a(3) corrected and a(33)-a(43) added by _Chai Wah Wu_, Apr 19 2022
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