jmc

We have 6 digits to choose from: 0, 1, 6, 7, 8, and 9. We therefore have 6 choices for each of the digits in a 4-digit number, where we think of numbers with fewer than four digits as having leading 0s. (For example, 0097 is 97.) Since we have 6 choices for each of the four digits in the number, there are $6^4=1296$ ways to form the number. However, we must exclude 0000 since this is not between 1 and 9999, inclusive, so there are $1296-1=\boxed{1295}$ numbers.