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Search: id:A077627
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| A077627 |
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Largest term in periodic part of continued fraction expansion of square root of -1+3^n. |
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+0
1
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| 2, 4, 10, 16, 30, 52, 92, 160, 280, 484, 840, 1456, 2524, 4372, 7574, 13120, 22726, 39364, 68182, 118096, 204550, 354292, 613654, 1062880, 1840964, 3188644, 5522896, 9565936, 16568690, 28697812
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OFFSET
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1,1
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FORMULA
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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
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MATHEMATICA
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Table[Max[Last[ContinuedFraction[Sqrt[ -1+3^u]]]], {u, 1, 32}]
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CROSSREFS
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Cf. A077624-A077635.
Sequence in context: A137928 A006584 A032246 this_sequence A117862 A105024 A050871
Adjacent sequences: A077624 A077625 A077626 this_sequence A077628 A077629 A077630
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KEYWORD
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nonn
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AUTHOR
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Labos E. (labos(AT)ana.sote.hu), Nov 13 2002
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