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

Offset

0,1

Comments

Not to be confused with the Pisot T(4,10) sequence, which is A020748. - R. J. Mathar, Feb 13 2016

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

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

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 *)

Prog

(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

Crossrefs

Sequence in context: A079859 A298802 A118871 * A192886 A079844 A080617

Adjacent sequences: A019491 A019492 A019493 * A019495 A019496 A019497

Keyword

nonn

Author

R. K. Guy

Status

approved