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A321541 a(0)=1; thereafter a(n) = 3*a(n-1) with digits rearranged into nonincreasing order.

%I A321541 #30 Aug 02 2024 15:55:58
%S A321541 1,3,9,72,621,8631,98532,996552,9986652,99996552,999986652,9999996552,
%T A321541 99999986652,999999996552,9999999986652,99999999996552,
%U A321541 999999999986652,9999999999996552,99999999999986652,999999999999996552,9999999999999986652,99999999999999996552,999999999999999986652
%N A321541 a(0)=1; thereafter a(n) = 3*a(n-1) with digits rearranged into nonincreasing order.
%C A321541 In contrast to A321542, this sequence increases forever.
%C A321541 Proof: The terms from a(7) onwards can be described as follows:
%C A321541 3 times the number 9 (2k times) 6552 is 2 9 (2k-1 times) 89656 which becomes 9 (2k times) 86652 when sorted;
%C A321541 then 3 times the number 9 (2k times) 86652 is 2 9 (2k times) 59956 which becomes 9 (2k+2 times) 6552 when sorted. QED
%H A321541 Paolo Xausa, <a href="/A321541/b321541.txt">Table of n, a(n) for n = 0..900</a>
%H A321541 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (10,1,-10).
%F A321541 From _Chai Wah Wu_, Nov 20 2018: (Start)
%F A321541 a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3) for n > 9.
%F A321541 G.f.: (118800*x^9 + 8910*x^8 + 8811*x^7 + 12321*x^6 + 2439*x^5 - 78*x^4 - 11*x^3 - 22*x^2 - 7*x + 1)/((x - 1)*(x + 1)*(10*x - 1)). (End)
%t A321541 NestList[FromDigits[ReverseSort[IntegerDigits[3*#]]] &, 1, 25] (* _Paolo Xausa_, Aug 02 2024 *)
%Y A321541 The following are parallel families: A000079 (2^n), A004094 (2^n reversed), A028909 (2^n sorted up), A028910 (2^n sorted down), A036447 (double and reverse), A057615 (double and sort up), A263451 (double and sort down); A000244 (3^n), A004167 (3^n reversed), A321540 (3^n sorted up), A321539 (3^n sorted down), A163632 (triple and reverse), A321542 (triple and sort up), A321541 (triple and sort down).
%K A321541 nonn,base
%O A321541 0,2
%A A321541 _N. J. A. Sloane_, Nov 19 2018