The equivalent -digit palindrome in base is 511999999.
To determine the largest possible -digit palindrome in base and its equivalent in another base, let's consider the following approach:
Largest Palindrome in Base:
The largest -digit palindrome in base can be constructed by filling the number with the highest possible digit of the base. In this case, the base is , so the largest possible digit is . Therefore, the largest -digit palindrome in base is .
Equivalent Palindrome in Base:
To find the equivalent -digit palindrome in base , we need to convert the base -digit number to base . This can be done using the following formula:
base10_number = base_b_number * b^(n-1) + ... + base_b_number * b^1 + base_b_number * b^0
where:
base10_number is the equivalent base -digit number
base_b_number is the given base -digit number
n is the number of digits in the base -digit number
b is the base
In this case, we have:
base10_number = 999999999 * 2^(9-1) + ... + 999999999 * 2^1 + 999999999 * 2^0 = 511999999
Therefore, the equivalent -digit palindrome in base is .