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

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

Crossrefs

Sequence in context: A023000 A331792 A097114 * A277671 A015453 A181246

Adjacent sequences: A022035 A022036 A022037 * A022039 A022040 A022041

Keyword

nonn

Author

R. K. Guy

Extensions

Incorrect g.f. deleted by Alois P. Heinz, Sep 18 2015

Status

approved