

A321541


a(0)=1; thereafter a(n) = 3*a(n1) with digits rearranged into nonincreasing order.


14



1, 3, 9, 72, 621, 8631, 98532, 996552, 9986652, 99996552, 999986652, 9999996552, 99999986652, 999999996552, 9999999986652, 99999999996552, 999999999986652, 9999999999996552, 99999999999986652, 999999999999996552, 9999999999999986652, 99999999999999996552, 999999999999999986652
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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 (2k1 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

Table of n, a(n) for n=0..22.


FORMULA

From Chai Wah Wu, Nov 20 2018: (Start)
a(n) = 10*a(n1) + a(n2)  10*a(n3) 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)


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 A018576 A027290
Adjacent sequences: A321538 A321539 A321540 * A321542 A321543 A321544


KEYWORD

nonn,base


AUTHOR

N. J. A. Sloane, Nov 19 2018


STATUS

approved



