The On-Line Encyclopedia of Integer Sequences (OEIS)

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A018919

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(3,9).
(history; published version)

#49 by Ray Chandler at Thu Jul 13 09:29:46 EDT 2023

STATUS

editing

approved

#48 by Ray Chandler at Thu Jul 13 09:29:42 EDT 2023

LINKS

<a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>

STATUS

approved

editing

#47 by Charles R Greathouse IV at Thu Sep 08 08:44:44 EDT 2022

PROG

(MAGMAMagma) Tiv:=[3, 9]; [n le 2 select Tiv[n] else Ceiling(Self(n-1)^2/Self(n-2))-1: n in [1..40]]; // Bruno Berselli, Feb 17 2016

Discussion

Thu Sep 08

08:44

OEIS Server: https://oeis.org/edit/global/2944

#46 by Harvey P. Dale at Wed Feb 06 11:24:52 EST 2019

STATUS

editing

approved

#45 by Harvey P. Dale at Wed Feb 06 11:24:48 EST 2019

MATHEMATICA

LinearRecurrence[{3, 0, -1}, {3, 9, 26}, 30] (* Harvey P. Dale, Feb 06 2019 *)

STATUS

approved

editing

#44 by N. J. A. Sloane at Fri Feb 19 06:54:54 EST 2016

STATUS

editing

approved

#43 by Bruno Berselli at Wed Feb 17 08:13:58 EST 2016

COMMENTS

Not to be confused with the Pisot LT(3,9) sequence, which is A000244. - R. J. Mathar, Feb 13 2016

#42 by Bruno Berselli at Wed Feb 17 08:05:53 EST 2016

MATHEMATICA

RecurrenceTable[{a[1] == 3, a[2] == 9, a[n] == Ceiling[a[n-1]^2/a[n-2]] - 1}, a, {n, 30}] (* Bruno Berselli, Feb 17 2016 *)

Discussion

Wed Feb 17

08:06

Bruno Berselli: Like A018918.

#41 by Bruno Berselli at Wed Feb 17 08:03:30 EST 2016

NAME

Define the generalized Pisot sequence LT(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 LT(3,9).

COMMENTS

Let M denotes the 4 X 4 matrix = row by row (1,1,1,1)(1,1,1,0)(1,1,0,0)(1,0,0,0) and A(n) the vector (x(n),y(n),z(n),t(n))=M^n*A where A is the vector (1,1,1,1) then a(n)=y(n+1) . - Benoit Cloitre, Apr 02 2002

PROG

(MAGMA) Tiv:=[3, 9]; [n le 2 select Tiv[n] else Ceiling(Self(n-1)^2/Self(n-2))-1: n in [1..40]]; // Bruno Berselli, Feb 17 2016

STATUS

approved

editing

#40 by Alois P. Heinz at Sun Feb 14 15:22:58 EST 2016

STATUS

proposed

approved