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

1,1

Comments

No formula is known to the author.

Links

Table of n, a(n) for n=1..15.

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

Example

a(2) = 99 * 91 = 9009, a(3) = 993 * 913 = 906609.

Prog

(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))

Crossrefs

Cf. A308803.

Sequence in context: A191961 A188965 A367517 * A249837 A240091 A263438

Adjacent sequences: A327894 A327895 A327896 * A327898 A327899 A327900

Keyword

nonn,base

Author

Christopher Shaw, Sep 29 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

Status

approved