999 (whole) numbers. THere are the same number whether they are counted in ascending, descending or other order.
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All numbers between 1000 and 2000, or anywhere else, can be expressed as a power of another number.
3000
1000+1000 1000x2
3 integers: 1200,1500,1800
1950 is between 1000 and 2000. 2000 is much closer, only 50 away. 1000 is 950 away. So 2000 is the answer.