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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

%I #39 Dec 06 2023 13:58:07

%S 4,11,30,81,218,586,1575,4233,11376,30572,82159,220793,593356,1594576,

%T 4285239,11516085,30948148,83169572,223508615,600653577,1614187084,

%U 4337941272,11657715927,31328764525,84192434676,226257439900,608040726071,1634039193249

%N 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).

%H Colin Barker, <a href="/A019495/b019495.txt">Table of n, a(n) for n = 0..1000</a>

%H D. W. Boyd, <a href="http://www.researchgate.net/publication/258834801_Linear_recurrence_relations_for_some_generalized_Pisot_sequences">Linear recurrence relations for some generalized Pisot sequences</a>, Advances in Number Theory (Kingston ON, 1991) 333-340, Oxford Sci. Publ., Oxford Univ. Press, New York, 1993.

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

%p a:= proc(n) option remember;

%p `if`(n<2, [4, 11][n+1], ceil(a(n-1)^2/a(n-2))-1)

%p end:

%p seq(a(n), n=0..30); # _Alois P. Heinz_, Sep 18 2015

%t a = {4, 11}; Do[AppendTo[a, Floor[a[[n]]^2/a[[n - 1]]]], {n, 2, 27}];

%t a (* _Michael De Vlieger_, Sep 18 2015 *)

%o (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

%o T(4, 11, 100) \\ _Colin Barker_, Sep 18 2015

%o (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

%o (Python)

%o from itertools import islice

%o def A019495_gen(): # generator of terms

%o a, b = 4, 11

%o yield from (a,b)

%o while True:

%o a, b = b, (b**2-1)//a

%o yield b

%o A019495_list = list(islice(A019495_gen(),30)) # _Chai Wah Wu_, Dec 06 2023

%Y See A008776 for definitions of Pisot sequences.

%K nonn

%O 0,1

%A _R. K. Guy_

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Last modified March 28 16:12 EDT 2024. Contains 371254 sequences. (Running on oeis4.)