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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.

%I A110843 #16 Feb 15 2023 14:02:34
%S A110843 1089,2178,21978,24024,2426424,240264024,23162643504,2305213214304
%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.
%C A110843 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
%C A110843 a(9) <= 2305213214304. a(10) <= 230316132350304. [From _Donovan Johnson_, Apr 09 2010]
%C A110843 The distinct prime factors of a(n) are a subset of the distinct prime factors of A056964(n). - _David A. Corneth_, Feb 15 2023
%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 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}]
%Y A110843 Cf. A056964.
%K A110843 base,hard,nonn
%O A110843 2,1
%A A110843 _Ryan Propper_, Sep 16 2005
%E A110843 a(7) from _Hans Havermann_, Sep 26 2005
%E A110843 a(8) from _Donovan Johnson_, Apr 09 2010
%E A110843 a(9) from _Michael S. Branicky_, Feb 15 2023