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A327897 a(n) is the largest palindromic number formed from two numbers with n digits multiplied together.

%I A327897 #38 Oct 04 2019 13:17:50
%S A327897 9,9009,906609,99000099,9966006699,999000000999,99956644665999,
%T A327897 9999000000009999,999900665566009999,99999834000043899999,
%U A327897 9999994020000204999999,999999000000000000999999,99999963342000024336999999,9999999000000000000009999999,999999974180040040081479999999
%N A327897 a(n) is the largest palindromic number formed from two numbers with n digits multiplied together.
%C A327897 No formula is known to the author.
%F A327897 a(n) = A308803(2*n) for n > 1. - _Andrew Howroyd_, Sep 30 2019
%F A327897 a(2n) >= (10^(2n)-1)*(10^(2n)-10^n+1). - _Chai Wah Wu_, Sep 30 2019
%e A327897 a(2) = 99 * 91 = 9009, a(3) = 993 * 913 = 906609.
%o A327897 (Python)
%o A327897 def is_palindrome(n):
%o A327897     if n<10: return True
%o A327897     n = str(n)
%o A327897     midpoint = int(len(n)/2)
%o A327897     return n[:midpoint] == n[-midpoint:][::-1]
%o A327897 def A327897(n):
%o A327897     lower_bound = 10**(n-1) - 1
%o A327897     upper_bound = 10**n - 1
%o A327897     max_palindromes = (0,0,0)
%o A327897     for n1 in range(upper_bound, lower_bound, -1):
%o A327897         for n2 in range(n1, lower_bound, -1):
%o A327897             n = n1* n2
%o A327897             if is_palindrome(n) and n>max_palindromes[2]:
%o A327897                 max_palindromes = (n1, n2, n)
%o A327897             if n < max_palindromes[2]:
%o A327897                 break
%o A327897         if n1*n1 < max_palindromes[2]:
%o A327897             break
%o A327897     return max_palindromes
%o A327897 if __name__ == '__main__':
%o A327897     for n in range(1,7):
%o A327897         print(A327897(n))
%Y A327897 Cf. A308803.
%K A327897 nonn,base
%O A327897 1,1
%A A327897 _Christopher Shaw_, Sep 29 2019
%E A327897 a(11) from _Chai Wah Wu_, Sep 30 2019
%E A327897 a(12) from _David A. Corneth_, Sep 30 2019
%E A327897 a(13)-a(15) from _Giovanni Resta_, Oct 04 2019