cp's OEIS Frontend

A022028 Define the sequence T(a(0),a(1)) by a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n) for n >= 0. This is T(2,32).

%I A022028 #22 Jul 13 2023 09:48:40
%S A022028 2,32,511,8160,130304,2080776,33227136,530591744,8472821696,
%T A022028 135299330048,2160544546816,34500930175488,550932488167424,
%U A022028 8797635454304256,140486159827464192,2243371097334087680,35823556473710968832,572053014300755787776,9134901260033419902976
%N A022028 Define the sequence T(a(0),a(1)) by a(n+2) is the greatest integer such that a(n+2)/a(n+1) < a(n+1)/a(n) for n >= 0. This is T(2,32).
%C A022028 Not to be confused with the Pisot T(2,32) sequence as defined in A008776, which is A013776. - _R. J. Mathar_, Feb 13 2016
%H A022028 Colin Barker, <a href="/A022028/b022028.txt">Table of n, a(n) for n = 0..830</a>
%H A022028 <a href="/index/Ph#Pisot">Index entries for Pisot sequences</a>
%F A022028 Conjecture: a(n) = 16*a(n-1)-8*a(n-3). G.f.: -(x^2-2) / (8*x^3-16*x+1). - _Colin Barker_, Sep 18 2015
%F A022028 a(n+1) = ceiling(a(n)^2/a(n-1))-1 for all n > 0. a(n+1)/a(n) ~ 15.968627... as n -> oo. - _M. F. Hasler_, Feb 11 2016
%o A022028 (PARI) a=[2,32];for(n=2,2000,a=concat(a,ceil(a[n]^2/a[n-1])-1));A022028(n)=a[n+1] \\ _M. F. Hasler_, Feb 11 2016
%Y A022028 Cf. A022018 - A022025, A022026 - A022032.
%K A022028 nonn
%O A022028 0,1
%A A022028 _R. K. Guy_