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A002813
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a(n) = a(n-1)^3 - 3*a(n-1)^2 + 3.
(Formerly M3561 N1443)
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1
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4, 19, 5779, 192900153619, 7177905237579946589743592924684179, 369822356418414944143680173221426891716916679027557977938929258031490127514207143830378340325399155219
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,1
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COMMENTS
| An infinite coprime sequence defined by recursion. - Michael Somos Mar 14 2004
The next term, a(7), has 305 digits. [From Harvey P. Dale, Jul 19 2011]
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REFERENCES
| L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 1, p. 397.
E. Lucas, Nouveaux theoremes d'arithmetique superieure, Comptes Rend., 83 (1876), 1286-1288.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..8
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FORMULA
| a(n)=L(2*3^n)+1 where L=Lucas numbers.
a(n)=L(3^(n+1))/L(3^n) - Benoit Cloitre, Sep 18 2005
a(n) = A001999(n)+1 - R. J. Mathar, Apr 22 2007
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MATHEMATICA
| NestList[#^3-3#^2+3&, 4, 6] (* From Harvey P. Dale, Jul 19 2011 *)
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PROG
| (PARI) a(n)=if(n<1, 4*(n==0), a(n-1)^3-3*a(n-1)^2+3)
(PARI) a(n)=if(n<0, 0, n=2*3^n; fibonacci(n+1)+fibonacci(n-1)+1)
(MAGMA) [Lucas(2*3^n)+1: n in [0..5]]; // Vincenzo Librandi, Jul 20 2011
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CROSSREFS
| Sequence in context: A000844 A000863 A023994 * A104159 A039921 A081852
Adjacent sequences: A002810 A002811 A002812 * A002814 A002815 A002816
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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