A022038 - OEIS

A022038

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(8,57).

8, 57, 406, 2891, 20585, 146572, 1043641, 7431068, 52911654, 376748420, 2682572954, 19100803803, 136004020087, 968393459804, 6895280686492, 49096671672207, 349584488128334, 2489156803863966, 17723617050044085, 126197996385357735, 898571338272012057

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..1171

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

MAPLE

a:= proc(n) option remember;

`if`(n<2, [8, 57][n+1], ceil(a(n-1)^2/a(n-2))-1)

end:

seq(a(n), n=0..30); # Alois P. Heinz, Sep 18 2015

MATHEMATICA

a[n_] := a[n] = Switch[n, 0, 8, 1, 57, _, Ceiling[a[n-1]^2/a[n-2]] - 1];

a /@ Range[0, 30] (* Jean-François Alcover, Nov 16 2020, after Alois P. Heinz *)

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(8, 57, 30) \\ Colin Barker, Feb 14 2016