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A327897 a(n) is the largest palindromic number formed from two numbers with n digits multiplied together. 3
9, 9009, 906609, 99000099, 9966006699, 999000000999, 99956644665999, 9999000000009999, 999900665566009999, 99999834000043899999, 9999994020000204999999, 999999000000000000999999, 99999963342000024336999999, 9999999000000000000009999999, 999999974180040040081479999999 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
No formula is known to the author.
LINKS
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
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

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Last modified April 25 03:15 EDT 2024. Contains 371964 sequences. (Running on oeis4.)