2,1

Comment from Hans Havermann, Sep 26 2005:

"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 a(n) always exists."

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.

r[n_] := 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}]

Sequence in context: A110819 A071685 A008919 this_sequence A023093 A001232 A039684

Adjacent sequences: A110840 A110841 A110842 this_sequence A110844 A110845 A110846

base,hard,nonn

Ryan Propper (rpropper(AT)stanford.edu), Sep 16 2005

a(7) from Hans Havermann, Sep 26 2005