There are an infinite number of them.
The smallest ten are:
They are members of an infinite set of numbers of the form 4000*k where k is an integer.
The multiples of 1,000 are an infinite number of integers in the set that begins 1000, 2000, 3000, 4000, and so on.
800, 1600, 2400, 3200, 4000, 4800, 5600, . . .
1000, 2000, 3000, 4000, 5000
500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, 5000, 5500, . . .
2000, 4000, 6000, 8000, 10000, 12000, 14000, 16000, . . .
They are: 500 1000 1500 2000 2500 3000 3500 4000 4500 and 5000
They are 500, 1000, 1500, 2000, 2500, 3000, 3500, 4000, 4500, and 5000.
3100 3200 3300 3400 3500 3600 3700 3800 3900
There are 50 multiples of 80 between 1 and 4000, as 4000 divided by 80 equals 50. However, the question asks for the number of occurrences of the digit "8" in the range from 1 to 4000, not the number of multiples of 80. The digit "8" appears in the units place for numbers 8, 18, 28, ..., 3998, occurring 500 times. Additionally, it appears in the tens place for numbers 80, 81, ..., 89, 180, 181, ..., 189, and so on, occurring 400 times. Therefore, the digit "8" appears 900 times in the range from 1 to 4000.
800, 1600, 2400, 3200, 4000, 4800, 5600, 6400, 7200, 8000, 8800, 9600, 10400, . . .
800, 1600, 2400, 3200, 4000, 4800, 5600, 6400, 7200, 8000, 8800, 9600, 10400, 11200, 12000.