The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 5 01:34 EDT 2024. Contains 373102 sequences. (Running on oeis4.)