A110843

[Hans Havermann]

> %I A110843
> %S A110843 1089,2178,21978,24024,2426424
> %N A110843 a(n) = least non-palindromic k such that k and r(k) have  
> the same n prime divisors, where r(k) is the digit reversal of k,  
> or 0 if no such integer exists.
> %e A110843 a(3) = 2178 because 2178 and 8712 both have the same 3  
> prime divisors, and 2178 is the least non-palindromic integer with  
> this property.
> %t A110843 FromDigits[Reverse[IntegerDigits[n]]]; Do[k = 1; While[r 
> [k] == k || Length[Select[Divisors[k], PrimeQ]] != n || Select 
> [Divisors[k], PrimeQ] != Select[Divisors[r[k]], PrimeQ], k++ ];  
> Print[k], {n, 2, 10}]
> %K A110843 base,hard,nonn,new
> %O A110843 2,1
> %A A110843 Ryan Propper (rpropper(AT)stanford.edu), Sep 16 2005


a(7) = 240264024

Noting that a(6) = a(5)*(10^2+1) and a(7) = a(5)*(10^4+1), we can  
derive an upper bound for a(n), n>7, of 24024*(10^x+1), where x is  
the smallest power that gives the number (10^x+1) exactly (n-5)  
factors-greater-than-13. For n = {8, 9, 10, 11, 12, 13, 14, 15, 16},  
this would be x = {10, 14, 16, 36, 30, 55, 45, 77, 70}. I think this  
upper limit exists for all n, so we can drop the qualifier in the  
definition. The Mathematica statement appears to be missing "r 
[n_] :=" at its start.