OFFSET
2,1
COMMENTS
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. - Hans Havermann, Sep 26 2005
a(9) <= 2305213214304. a(10) <= 230316132350304. [From Donovan Johnson, Apr 09 2010]
The distinct prime factors of a(n) are a subset of the distinct prime factors of A056964(n). - David A. Corneth, Feb 15 2023
EXAMPLE
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.
MATHEMATICA
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}]
CROSSREFS
KEYWORD
base,hard,nonn
AUTHOR
Ryan Propper, Sep 16 2005
EXTENSIONS
a(7) from Hans Havermann, Sep 26 2005
a(8) from Donovan Johnson, Apr 09 2010
a(9) from Michael S. Branicky, Feb 15 2023
STATUS
approved