|
%I #13 Sep 22 2017 15:42:41
%S 9,17,32,60,113,213,401,755,1422,2678,5043,9497,17885,33682,63432,
%T 119459,224972,423680,797898,1502646,2829867,5329364,10036557,
%U 18901407,35596190,67036742,126247353,237756097,447755619,843238499,1588034044,2990674795,5632206541
%N Pisot sequence E(9,17), a(n) = floor( a(n-1)^2/a(n-2) + 1/2 ).
%H Colin Barker, <a href="/A014004/b014004.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.
%F Known not to satisfy any linear recurrence.
%t nxt[{a_,b_}]:={b,Floor[b^2/a+1/2]}; NestList[nxt,{9,17},40][[All,1]] (* _Harvey P. Dale_, Sep 22 2017 *)
%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, 9, 17) \\ _Colin Barker_, Jul 28 2016
%K nonn
%O 0,1
%A _Simon Plouffe_
|
