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Pisot sequence E(8,10), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).
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%I #21 Sep 19 2016 21:47:31

%S 8,10,13,17,22,28,36,46,59,76,98,126,162,208,267,343,441,567,729,937,

%T 1204,1547,1988,2555,3284,4221,5425,6972,8960,11515,14799,19020,24445,

%U 31417,40377,51892,66691,85711,110155,141570,181944,233832,300518,386222,496368,637926

%N Pisot sequence E(8,10), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).

%D Cantor, D. G. "Investigation of T-numbers and E-sequences." In Computers in Number Theory, ed. AOL Atkin and BJ Birch, Acad. Press, NY (1971); pp. 137-140.

%H Colin Barker, <a href="/A010916/b010916.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/profile/David_Boyd7/publication/262181133_Linear_recurrence_relations_for_some_generalized_Pisot_sequences_-_annotated_with_corrections_and_additions/links/00b7d536d49781037f000000.pdf">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 David Cantor, <a href="/A010900/a010900.pdf">Investigation of T-numbers and E-sequences</a>, In Computers in Number Theory, ed. A. O. L. Atkin and B. J. Birch, Acad. Press, NY (1971); pp. 137-140. [Annotated scanned copy]

%F It is not true that a(n) = a(n-1) + a(n-6), which holds just for n <= 37 (see A275627). E.g. a(38) = 110155 = 85711 + 24445 - 1 = a(37) + a(32) - 1. Sequence is believed to be non-recurring.

%o (PARI) pisotE(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]+1/2));

%o a

%o }

%o pisotE(50, 8, 10) \\ _Colin Barker_, Jul 28 2016

%Y See A008776 for definitions of Pisot sequences.

%Y Cf. A275627.

%K nonn

%O 0,1

%A _Simon Plouffe_