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Search: id:A018906
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| A018906 |
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Define the Shallit sequence S(a_0,a_1) by a_{n+2} is the least integer > a_{n+1}^2/a_n for n >= 0 . This is S(2,6). |
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2
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| 2, 6, 19, 61, 196, 630, 2026, 6516, 20957, 67403, 216786, 697242, 2242518, 7212542, 23197479, 74609345, 239963764, 771788146, 2482278709, 7983677414, 25677658524, 82586271099, 265619708576, 854304579262
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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D. W. Boyd, Some integer sequences related to the Pisot sequences, Acta Arithmetica, 34 (1979), 295-305.
D. W. Boyd, Linear recurrence relations for some generalized Pisot sequences, Advances in Number Theory ( Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.
Problem B-686, Fib. Quart., 29 (1991), 85.
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FORMULA
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a(n)=[ a(n-1)^2/a(n-2)+1 ].
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PROGRAM
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(PARI) a1n=concat([ 2, 6 ], vector(28)); a(n)=a1n[ n+1 ]; for(n=2, 29, a1n[ n+1 ]=1+floor(a(n-1)^2/a(n-2)))
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CROSSREFS
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There has been some confusion between A018906 and A014010. I think the descriptions are correct now, thanks to Michael Somos
Sequence in context: A052544 A001169 A022041 this_sequence A014010 A022015 A138747
Adjacent sequences: A018903 A018904 A018905 this_sequence A018907 A018908 A018909
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KEYWORD
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nonn
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AUTHOR
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Simon Plouffe, R. K. Guy (rkg(AT)cpsc.ucalgary.ca)
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EXTENSIONS
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An incorrect g.f. was deleted by N. J. A. Sloane, Sep 16 2009
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