A019495 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(4,11).

4, 11, 30, 81, 218, 586, 1575, 4233, 11376, 30572, 82159, 220793, 593356, 1594576, 4285239, 11516085, 30948148, 83169572, 223508615, 600653577, 1614187084, 4337941272, 11657715927, 31328764525, 84192434676, 226257439900, 608040726071, 1634039193249

Offset

0,1

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

Maple

a:= proc(n) option remember;
      `if`(n<2, [4, 11][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 = {4, 11}; Do[AppendTo[a, Floor[a[[n]]^2/a[[n - 1]]]], {n, 2, 27}];
a (* Michael De Vlieger, Sep 18 2015 *)

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(4, 11, 100) \\ Colin Barker, Sep 18 2015
(Magma) Iv:=[4, 11]; [n le 2 select Iv[n] else Floor(Self(n-1)^2/Self(n-2)): n in [1..40]]; // Bruno Berselli, Feb 04 2016
(Python)
from itertools import islice
def A019495_gen(): # generator of terms
    a, b = 4, 11
    yield from (a, b)
    while True:
        a, b = b, (b**2-1)//a
        yield b
A019495_list = list(islice(A019495_gen(), 30)) # Chai Wah Wu, Dec 06 2023

Crossrefs

See A008776 for definitions of Pisot sequences.

Sequence in context: A114726 A128098 A341104 * A019496 A021006 A078141

Adjacent sequences: A019492 A019493 A019494 * A019496 A019497 A019498

Keyword

nonn

Author

R. K. Guy

Status

approved