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A305880 A base 3/2 reverse sorted Fibonacci sequence that starts with terms 2211 and 2211. The terms are interpreted as numbers written in base 3/2. To get a(n+2), add a(n) and a(n+1), write the result in base 3/2 and sort the digits into decreasing order, omitting all zeros.

%I A305880 #54 Jun 24 2018 14:42:26
%S A305880 2211,2211,22211,22211,222211,222211,2222211,2222211,22222211,
%T A305880 22222211,222222211,222222211,2222222211,2222222211,22222222211,
%U A305880 22222222211,222222222211,222222222211,2222222222211,2222222222211,22222222222211,22222222222211
%N A305880 A base 3/2 reverse sorted Fibonacci sequence that starts with terms 2211 and 2211. The terms are interpreted as numbers written in base 3/2. To get a(n+2), add a(n) and a(n+1), write the result in base 3/2 and sort the digits into decreasing order, omitting all zeros.
%C A305880 a(2n-1) and a(2n) consist of n+1 2's followed by 2 1's.
%C A305880 If a reverse sorted Fibonacci sequence starts with any two numbers, then it eventually becomes either cyclic or turns into this sequence.
%C A305880 In base 10, the corresponding sequence is A069638 and is periodic.
%H A305880 Colin Barker, <a href="/A305880/b305880.txt">Table of n, a(n) for n = 1..1000</a>
%H A305880 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,10,-10).
%F A305880 From _Colin Barker_, Jun 19 2018: (Start)
%F A305880 G.f.: x*(2211 - 2110*x^2) / ((1 - x)*(1 - 10*x^2)).
%F A305880 a(n) = (2^((n+5)/2+3/2) * 5^((n+5)/2+1/2) - 101) / 9 for n even.
%F A305880 a(n) = (2^((n+9)/2) * 5^((n+7)/2) - 101) / 9 for n odd.
%F A305880 a(n) = a(n-1) + 10*a(n-2) - 10*a(n-3) for n>3.
%F A305880 (End)
%e A305880 2211 + 2211 equals 210122 when all numbers are interpreted in base 3/2; after sorting and omitting 0's we obtain a(2) = 22211.
%e A305880 (A305753 has more detailed examples which may help explain the calculations here. - _N. J. A. Sloane_, Jun 22 2018)
%Y A305880 Cf. A000045, A024629, A069638, A237575, A305753.
%K A305880 nonn,base
%O A305880 1,1
%A A305880 _Tanya Khovanova_ and PRIMES STEP Senior group, Jun 13 2018