A327897 a(n) is the largest palindromic number formed from two numbers with n digits multiplied together.
9, 9009, 906609, 99000099, 9966006699, 999000000999, 99956644665999, 9999000000009999, 999900665566009999, 99999834000043899999, 9999994020000204999999, 999999000000000000999999, 99999963342000024336999999, 9999999000000000000009999999, 999999974180040040081479999999
Offset: 1
Examples
a(2) = 99 * 91 = 9009, a(3) = 993 * 913 = 906609.
Crossrefs
Cf. A308803.
Programs
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Python
def is_palindrome(n): if n<10: return True n = str(n) midpoint = int(len(n)/2) return n[:midpoint] == n[-midpoint:][::-1] def A327897(n): lower_bound = 10**(n-1) - 1 upper_bound = 10**n - 1 max_palindromes = (0,0,0) for n1 in range(upper_bound, lower_bound, -1): for n2 in range(n1, lower_bound, -1): n = n1* n2 if is_palindrome(n) and n>max_palindromes[2]: max_palindromes = (n1, n2, n) if n < max_palindromes[2]: break if n1*n1 < max_palindromes[2]: break return max_palindromes if _name_ == '_main_': for n in range(1,7): print(A327897(n))
Formula
a(n) = A308803(2*n) for n > 1. - Andrew Howroyd, Sep 30 2019
a(2n) >= (10^(2n)-1)*(10^(2n)-10^n+1). - Chai Wah Wu, Sep 30 2019
Extensions
a(11) from Chai Wah Wu, Sep 30 2019
a(12) from David A. Corneth, Sep 30 2019
a(13)-a(15) from Giovanni Resta, Oct 04 2019
Comments