A022039 Define the generalized Pisot 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). This is T(8,65).

8, 65, 528, 4288, 34823, 282798, 2296605, 18650749, 151462893, 1230031456, 9989096027, 81121534697, 658788680558, 5350028537458, 43447627739097, 352838558325161, 2865404964997647, 23269978350457597, 188975694202166613, 1534673236964508227

Offset

0,1

Comments

This coincides with the Pisot T(8,65) sequence as defined in A008776 at least up to n <= 14000. - R. J. Mathar, Feb 13 2016

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for Pisot sequences

Formula

Empirical g.f.: -(x^6+x^5+x^4+x^3-x-8) / (x^7+x^6+x^5+x^4-x^2-8*x+1). - Colin Barker, Dec 02 2014

Mathematica

RecurrenceTable[{a[1] == 8, a[2] == 65, a[n] == Ceiling[a[n-1]^2/a[n-2]] - 1}, a, {n, 30}] (* Bruno Berselli, Feb 17 2016 *)

Prog

(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(8, 65, 100) \\ Colin Barker, Dec 02 2014
(Magma) Tiv:=[8, 65]; [n le 2 select Tiv[n] else Ceiling(Self(n-1)^2/Self(n-2))-1: n in [1..30]]; // Bruno Berselli, Feb 17 2016

Crossrefs

Sequence in context: A288788 A033118 A033126 * A041025 A163459 A081190

Adjacent sequences: A022036 A022037 A022038 * A022040 A022041 A022042

Keyword

nonn

Author

R. K. Guy

Status

approved