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A022025 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(6,102).

%I A022025 #40 Jul 13 2023 09:47:06
%S A022025 6,102,1735,29513,502028,8539699,145263729,2470994700,42032617843,
%T A022025 714991805825,12162299391068,206885624804179,3519208035780561,
%U A022025 59863150041598764,1018296359995701043,17321632357467588641,294647962336362325244,5012080843035687303187
%N A022025 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(6,102).
%H A022025 Alois P. Heinz, <a href="/A022025/b022025.txt">Table of n, a(n) for n = 0..811</a>
%H A022025 D. W. Boyd, <a href="http://www.researchgate.net/publication/258834801_Linear_recurrence_relations_for_some_generalized_Pisot_sequences">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 A022025 <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%F A022025 The conjectured g.f. (6-5*x^2)/(1-17*x-x^2+14*x^3) yields the same initial terms a(0..271) but from a(272) on a different sequence. - _Bruno Berselli_ and _M. F. Hasler_, Feb 11 2016
%F A022025 a(n+1) = floor(a(n)^2/a(n-1))+1 for all n > 0. - _M. F. Hasler_, Feb 10 2016
%p A022025 a:= proc(n) option remember;
%p A022025       `if`(n<2, [6, 102][n+1], floor(a(n-1)^2/a(n-2))+1)
%p A022025     end:
%p A022025 seq(a(n), n=0..20);  # _Alois P. Heinz_, Sep 18 2015
%t A022025 a[n_] := a[n] = Switch[n, 0, 6, 1, 102, _, 1 + Floor[a[n-1]^2/a[n-2]]];
%t A022025 a /@ Range[0, 20] (* _Jean-François Alcover_, Nov 16 2020, after _Alois P. Heinz_ *)
%o A022025 (PARI) a=[6,102];for(n=2,30,a=concat(a,a[n]^2\a[n-1]+1));a \\ _M. F. Hasler_, Feb 10 2016
%Y A022025 Cf. A022018 - A022024, A022026 - A022032.
%K A022025 nonn
%O A022025 0,1
%A A022025 _R. K. Guy_
%E A022025 An incorrect program was removed by _Alois P. Heinz_, Apr 27 2019