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A006266
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A continued cotangent.
(Formerly M2073)
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16
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OFFSET
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0,1
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COMMENTS
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The next (6th) term is 280 digits long. - M. F. Hasler, Oct 06 2014
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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G. C. Greubel, Table of n, a(n) for n = 0..7
J. Shallit, Predictable regular continued cotangent expansions, J. Res. Nat. Bur. Standards Sect. B 80B (1976), no. 2, 285-290.
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FORMULA
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From Artur Jasinski, Sep 24 2008: (Start)
a(n+1) = a(n)^3 + 3*a(n) with a(0)=2.
a(n) = round((1+sqrt(2))^(3^n)). [Corrected by M. F. Hasler, Oct 06 2014] (End)
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MATHEMATICA
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Table[Round[(1+Sqrt[2])^(3^n)], {n, 0, 10}] (* Artur Jasinski, Sep 24 2008 *)
LucasL[3^Range[0, 7], 2] (* G. C. Greubel, Mar 25 2022 *)
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PROG
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(PARI) a(n, s=2)=for(i=2, n, s*=(s^2+3)); s \\ M. F. Hasler, Oct 06 2014
(Magma) [Evaluate(DicksonFirst(3^n, -1), 2): n in [0..7]]; // G. C. Greubel, Mar 25 2022
(Sage) [lucas_number2(3^n, 2, -1) for n in (0..7)] # G. C. Greubel, Mar 25 2022
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CROSSREFS
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Cf. A006267. - Artur Jasinski, Sep 24 2008
Cf. A145451, A145452.
Sequence in context: A277288 A296412 A296410 * A284378 A106484 A228342
Adjacent sequences: A006263 A006264 A006265 * A006267 A006268 A006269
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane
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EXTENSIONS
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Edited by M. F. Hasler, Oct 06 2014
Offset corrected by G. C. Greubel, Mar 25 2022
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STATUS
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approved
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