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A019495
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Define the sequence T(a(0),a(1)) by a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n) for n >= 0. This is T(4,11).
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2
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4, 11, 30, 81, 218, 586, 1575, 4233, 11376, 30572, 82159, 220793, 593356, 1594576, 4285239, 11516085, 30948148, 83169572, 223508615, 600653577, 1614187084, 4337941272, 11657715927, 31328764525, 84192434676, 226257439900, 608040726071, 1634039193249
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OFFSET
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0,1
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LINKS
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Colin Barker, Table of n, a(n) for n = 0..1000
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.
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MAPLE
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a:= proc(n) option remember;
`if`(n<2, [4, 11][n+1], ceil(a(n-1)^2/a(n-2))-1)
end:
seq(a(n), n=0..30); # Alois P. Heinz, Sep 18 2015
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MATHEMATICA
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a = {4, 11}; Do[AppendTo[a, Floor[a[[n]]^2/a[[n - 1]]]], {n, 2, 27}];
a (* Michael De Vlieger, Sep 18 2015 *)
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PROG
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(PARI) T(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=floor(a[n-1]^2/a[n-2])); a
T(4, 11, 100) \\ Colin Barker, Sep 18 2015
(Magma) Iv:=[4, 11]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..40]]; // Bruno Berselli, Feb 04 2016
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CROSSREFS
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See A008776 for definitions of Pisot sequences.
Sequence in context: A114726 A128098 A341104 * A019496 A021006 A078141
Adjacent sequences: A019492 A019493 A019494 * A019496 A019497 A019498
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KEYWORD
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nonn
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AUTHOR
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R. K. Guy
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STATUS
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approved
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