There are 105 numbers in the the first 1000 positive integers contain only 0s and 1s when written in base 3
The number base is given as:
Base 3
To determine the count of numbers, we make use of the following Python program
count = 0
for n in range(1,1001):
digits = []
while n:
digits.append(int(n % 3))
n //= 3
myStr = ''.join(map(str,digits[::-1]))
if(myStr.count('0')+myStr.count('1') == len(myStr)):
count+=1
print(count)
The above program counts the numbers in the the first 1000 positive integers contain only 0s and 1s when written in base 3
The output of the program is 105
Hence, there are 105 numbers in the the first 1000 positive integers contain only 0s and 1s when written in base 3
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