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

0,2

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).

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)

Mathematica

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

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).

Sequence in context: A004167 A321539 A163632 * A102322 A305855 A018576

Adjacent sequences: A321538 A321539 A321540 * A321542 A321543 A321544

Keyword

nonn,base

Author

N. J. A. Sloane, Nov 19 2018

Status

approved