Can anybody be kind enough to explain what exactly is a super palindrome?
Also consider the following example :
$923456781-123456789=799999992:9=88888888$
The largest prime factor of $88888888$ is $137$
$88888888:137=648824:101$ ($101$ being largest prime factor of $648824$) = $6424:73$ ($73$ being largest prime factor of $6424$) this in turn equals to $88$ (a palindrome)
Finally, $88:11$ ($11$ being largest prime factor of 88 and a palindrome) equals to $8$ which is also a palindrome.
Now, given this post and its comments, will it be correct to call $88888888$ a super palindrome?
Can it be possible to call a number a super palindrome if it generates non palindromes along with palindromes, provided the non-palindromes finally generate using the method of division by largest prime factor, a palindrome other than 1?
Best Answer
Based on the linked post's definition of super-palindrome:
"I define a super-palindrome as a palindrome which is either 1, or which gives another super-palindrome if divided by its largest prime factor."
88888888 is not a super palindrome since division by its largest prime factor does not yield another super-palindrome. Also, you ended your algorithm early by stopping at 8 since you can say the largest prime factor of 8 is 2 etc. Your number still seems to exhibit interesting properties however and would certainly warrant more investigation!
For example, any $n$-digit number with all of its digits a single number has the same prime divisors as the other 8 $n$-digit numbers with all their digits the same. Also note that your numbers are nearly symmetric upon division of their largest prime factor. If you provided a more rigorous definition of this, that could be interesting to study.
Just some thoughts.