# concatenation of the numbers in sequences

Let us define the sequence $s_n$ obtained through the concatenation of the first $n$ positive integers in reverse order.

From $A000422$ in $OEIS,$

we can have the following sequence:

$1, 21, 321, 4321, 54321, 654321, 7654321, 87654321, 987654321, 10987654321, 1110987654321, 121110987654321, 13121110987654321, 1413121110987654321, 151413121110987654321, 16151413121110987654321, 1716151413121110987654321, …$

Here the primes appear very rare among the terms of this sequence too: until now there are only two known, corresponding to $n = 82$ (a number having $155$ digits) and $n = 37765$ (a number having $177719$ digits).

Now the question is:

Generalize the following statement:

"The number $n$ of the base $10$ reverse sequence is not square-free if $n$ is congruent to $0$ or $8$ modulo $9$."

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