Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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 $9$."

share|improve this question
    
Welcome to math.SE: since you are new, I wanted to let you know a few things about the site. In order to get the best possible answers, it is helpful if you say in what context you encountered the problem, and what your thoughts on it are; this will prevent people from telling you things you already know, and help them give their answers at the right level. If this is homework, please add the homework tag; people will still help, so don't worry. Also, many find the use of imperative ("Generalize",, etc.) to be rude when asking for help; please consider rewriting your post. –  Matthew Conroy Jan 2 at 20:39

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.