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A077631
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Sum of terms in periodic part of continued fraction expansion of square root of -1 + 3^n.
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1
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2, 5, 10, 17, 56, 53, 160, 161, 346, 485, 1850, 1457, 3764, 4373, 13468, 13121, 43572, 39365, 192642, 118097, 226348, 354293, 2646006, 1062881, 1871694, 3188645, 5646564, 9565937, 36393508, 28697813, 143274092, 86093441, 195407590, 258280325, 542628818, 774840977
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OFFSET
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1,1
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LINKS
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FORMULA
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a(2n) = 2*3^n-1.
Conjecture: if n>1 sqrt(3^(2n+1)) < a(2n+1) < sqrt((2n+1)*3^(2n+1)). (End)
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MATHEMATICA
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Table[Apply[Plus, Last[ContinuedFraction[Sqrt[ -1+3^u]]]], {u, 1, 25}]
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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