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%I #26 Aug 09 2016 03:11:30
%S 14,23,38,63,104,172,284,469,775,1281,2117,3499,5783,9558,15797,26109,
%T 43152,71320,117875,194819,321989,532170,879548,1453680,2402581,
%U 3970885,6562912,10846905,17927308,29629500,48970390,80936199,133767942,221086022,365401668
%N Pisot sequence E(14,23), a(n) = floor( a(n-1)^2/a(n-2)+1/2 ).
%H Colin Barker, <a href="/A010902/b010902.txt">Table of n, a(n) for n = 0..1000</a>
%H D. W. Boyd, <a href="http://matwbn.icm.edu.pl/ksiazki/aa/aa32/aa32110.pdf">Pisot sequences which satisfy no linear recurrences</a>, Acta Arith. 32 (1) (1977) 89-98
%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 It is known (Boyd, 1977) that this sequence does not satisfy a linear recurrence. - _N. J. A. Sloane_, Aug 07 2016
%t RecurrenceTable[{a[1] == 14, a[2] == 23, a[n] == Floor[a[n-1]^2/a[n-2]+1/2]}, a, {n, 40}] (* _Vincenzo Librandi_, Aug 09 2016 *)
%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, 14, 23) \\ _Colin Barker_, Jul 28 2016
%o (Python)
%o a, b = 14, 23
%o A010902_list = [a, b]
%o for i in range(1000):
%o c, d = divmod(b**2, a)
%o a, b = b, c + (0 if 2*d < a else 1)
%o A010902_list.append(b) # _Chai Wah Wu_, Aug 08 2016
%Y Cf. A008776.
%K nonn
%O 0,1
%A _Simon Plouffe_
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