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%I #27 Jul 13 2023 09:36:38
%S 2,10,51,261,1336,6839,35009,179212,917391,4696149,24039712,123059927,
%T 629947050,3224715759,16507406022,84501851928,432567234958,
%U 2214323218841,11335179646638,58025087091309,297031969224468,1520514576781740,7783554693597965
%N Define the sequence S(a(0),a(1)) by a(n+2) is the least integer such that a(n+2)/a(n+1) > a(n+1)/a(n) for n >= 0. This is S(2,10).
%H Alois P. Heinz, <a href="/A019475/b019475.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</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, [2, 10][n+1], floor(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[n_] := a[n] = Switch[n, 0, 2, 1, 10, _, 1 + Floor[a[n-1]^2/a[n-2]]];
%t a /@ Range[0, 30] (* _Jean-François Alcover_, Nov 16 2020, after _Alois P. Heinz_ *)
%o (PARI) S(a0, a1, maxn) = a=vector(maxn); a[1]=a0; a[2]=a1; for(n=3, maxn, a[n]=a[n-1]^2\a[n-2]+1); a
%o S(2, 10, 40) \\ _Colin Barker_, Feb 16 2016
%K nonn
%O 0,1
%A _R. K. Guy_
%E Incorrect g.f. deleted by _Alois P. Heinz_, Sep 18 2015
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