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Largest term in periodic part of continued fraction expansion of square root of -1+3^n.
1

%I #8 Oct 01 2019 15:40:06

%S 2,4,10,16,30,52,92,160,280,484,840,1456,2524,4372,7574,13120,22726,

%T 39364,68182,118096,204550,354292,613654,1062880,1840964,3188644,

%U 5522896,9565936,16568690,28697812,49706070,86093440,149118214,258280324,447354646,774840976,1342063940

%N Largest term in periodic part of continued fraction expansion of square root of -1+3^n.

%H Chai Wah Wu, <a href="/A077627/b077627.txt">Table of n, a(n) for n = 1..57</a>

%F a(2*m) = 2*(3^m-1); in general a(n) is close to 2*(3^(n/2)-1) and for any n, 0 <= a(n) - 2*(3^(n/2)-1) < 2. Conjecture: a(n)=ceiling(2*(3^(n/2)-1)) except for n=3, 9, 27 and all powers of 3, in this case a(n)=1+ceiling(2*(3^(n/2)-1)). - Benoit Cloitre, Nov 24 2002

%t Table[Max[Last[ContinuedFraction[Sqrt[ -1+3^u]]]], {u, 1, 32}]

%Y Cf. A077624-A077635.

%K nonn

%O 1,1

%A _Labos Elemer_, Nov 13 2002

%E a(31)-a(37) from _Chai Wah Wu_, Oct 01 2019