What is the logic behind the sequence 61, 21, 82, 43, 3, 64, and 24?

Answer 1

The series is multiples of six written together side by side and grouped 2 at a time as shown below.
[(6)(1][2)(1][8)(2][4)(3][0)(3][6)(4][2)(4][8)(5][4)(6][0) & so on.

Answer 2

If you remove all commas and add one 0 and 8, you get multiples of 6: 6-12-18-24-30-36-42-48