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Largest term in periodic part of continued fraction expansion of square root of -1+2^n or 0 if -1+2^n is square.
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%I #15 Apr 25 2022 08:04:14

%S 0,2,4,6,10,14,22,30,44,62,90,126,180,254,362,510,724,1022,1448,2046,

%T 2896,4094,5792,8190,11584,16382,23170,32766,46340,65534,92680,131070,

%U 185362,262142,370726,524286,741454,1048574,1482910,2097150,2965820,4194302,5931640

%N Largest term in periodic part of continued fraction expansion of square root of -1+2^n or 0 if -1+2^n is square.

%C a(n) = 0 iff n = 1, as a consequence of Catalan's conjecture or Mihăilescu's theorem. - _Bernard Schott_, Apr 24 2022

%H Chai Wah Wu, <a href="/A077625/b077625.txt">Table of n, a(n) for n = 1..80</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Catalan&#39;s_conjecture">Catalan's conjecture</a>.

%t Table[Max[Last[ContinuedFraction[Sqrt[ -1+2^u]]]], {u, 1, 32}]

%Y Cf. A077624-A077635.

%K nonn

%O 1,2

%A _Labos Elemer_, Nov 13 2002

%E Definition clarified, a(1) corrected and a(33)-a(43) added by _Chai Wah Wu_, Apr 19 2022