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%I #34 Oct 16 2021 05:22:40
%S 8,55,379,2612,18002,124071,855106,5893451,40618081,279942687,
%T 1929384798,13297456486,91647010581,631637678776,4353291555505,
%U 30003193292641,206784130187015,1425170850320396,9822378297435246,67696525926163327,466569244606302614
%N Shallit sequence S(8,55): a(n) = floor(a(n-1)^2/a(n-2) + 1).
%C Agrees with A019484 for terms 0 through 11055 but then differs from it. It is not known if S(8,55) satisfies a linear recurrence.
%C a(11056) = 4971494197...7586894095 (9270 digits) = A019484(11056) + 1. - _Jianing Song_, Oct 15 2021
%H Colin Barker, <a href="/A010918/b010918.txt">Table of n, a(n) for n = 0..1000</a>
%H D. W. Boyd, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa34/aa3444.pdf">Some integer sequences related to the Pisot sequences</a>, Acta Arithmetica, 34 (1979), 295-305.
%H D. W. Boyd, <a href="https://www.researchgate.net/publication/262181133_Linear_recurrence_relations_for_some_generalized_Pisot_sequences_-_annotated_with_corrections_and_additions">Linear recurrence relations for some generalized Pisot sequences</a>, in Advances in Number Theory (Kingston ON, 1991), pp. 333-340, Oxford Univ. Press, New York, 1993; with updates from 1996 and 1999.
%H Jeffrey Shallit, <a href="http://www.fq.math.ca/Scanned/29-1/elementary29-1.pdf">Problem B-686</a>, Fib. Quart., 29 (1991), 85.
%H <a href="/index/Se#sequences_which_agree_for_a_long_time">Index entries for sequences which agree for a long time but are different</a>
%o (PARI) pisotS(nmax, a1, a2) = {
%o a=vector(nmax); a[1]=a1; a[2]=a2;
%o for(n=3, nmax, a[n] = floor(a[n-1]^2/a[n-2]+1));
%o a
%o }
%o pisotS(50, 8, 55) \\ _Colin Barker_, Aug 09 2016
%K nonn
%O 0,1
%A _N. J. A. Sloane_ and _Simon Plouffe_
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