A019494 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(4,10).
4, 10, 24, 57, 135, 319, 753, 1777, 4193, 9893, 23341, 55069, 129925, 306533, 723205, 1706261, 4025589, 9497589, 22407701, 52866581, 124728341, 294272085, 694277333, 1638011349, 3864566869, 9117688405, 21511399509, 50751932757, 119739242325, 282501283669
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Keywords
Links
- 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.
- Index entries for Pisot sequences
Programs
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Mathematica
T[a_, b_, n_] := Block[{s = {a, b}, k}, Do[k = Ceiling[b Last@ s/a]; While[k/s[[i - 1]] >= s[[i - 1]]/s[[i - 2]], k--]; AppendTo[s, k], {i, 3, n}]; s]; T[4, 10, 20] (* or *) a = {4, 10}; Do[AppendTo[a, Ceiling[a[[n - 1]]^2/a[[n - 2]]] - 1], {n, 3, 27}]; a (* Michael De Vlieger, Feb 15 2016 *) -
PARI
T(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=ceil(a[n-1]^2/a[n-2])-1); a T(4, 10, 30) \\ Colin Barker, Feb 16 2016
Formula
Empirical G.f.: (4-2*x+2*x^2-3*x^3)/(1-3*x+2*x^2-2*x^3+2*x^4). - Colin Barker, Feb 04 2012
a(n+1) = ceiling(a(n)^2/a(n-1))-1 for n>0. - Bruno Berselli, Feb 15 2016
Comments