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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). 2
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,1
LINKS
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.
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified April 18 18:58 EDT 2024. Contains 371781 sequences. (Running on oeis4.)