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

1, 3, 9, 72, 621, 8631, 98532, 996552, 9986652, 99996552, 999986652, 9999996552, 99999986652, 999999996552, 9999999986652, 99999999996552, 999999999986652, 9999999999996552, 99999999999986652, 999999999999996552, 9999999999999986652, 99999999999999996552, 999999999999999986652

Offset: 0

Author

N. J. A. Sloane, Nov 19 2018

Keywords

• nonn
• base

Comments

In contrast to A321542, this sequence increases forever.

Proof: The terms from a(7) onwards can be described as follows:

3 times the number 9 (2k times) 6552 is 2 9 (2k-1 times) 89656 which becomes 9 (2k times) 86652 when sorted;

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

Links

• Paolo Xausa, Table of n, a(n) for n = 0..900
• Index entries for linear recurrences with constant coefficients, signature (10,1,-10).

Crossrefs

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).

Programs

Mathematica

NestList[FromDigits[ReverseSort[IntegerDigits[3*#]]] &, 1, 25] (* Paolo Xausa, Aug 02 2024 *)

Formula

From Chai Wah Wu, Nov 20 2018: (Start)

a(n) = 10*a(n-1) + a(n-2) - 10*a(n-3) for n > 9.

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)