1. The problem is to find another 6-digit number that exhibits the same cyclic behavior as 142857 when multiplied or added repeatedly. 2. The number 142857 is the cyclic number generated by the fraction $\frac{1}{7}$. 3. Other cyclic numbers arise from fractions with prime denominators where the decimal expansion repeats with length equal to the prime minus one. 4. For example, the fraction $\frac{1}{13}$ has a repeating decimal of length 6: $0.076923076923...$ and the repeating part is 076923. 5. Multiplying 076923 by integers 1 through 6 cycles through permutations: $$ 076923 \times 1 = 076923 $$ $$ 076923 \times 2 = 153846 $$ $$ 076923 \times 3 = 230769 $$ $$ 076923 \times 4 = 307692 $$ $$ 076923 \times 5 = 384615 $$ $$ 076923 \times 6 = 461538 $$ 6. Thus, 076923 is another 6-digit cyclic number with the same behavior. Final answer: Another 6-digit number with the same cyclic behavior is 076923, the repeating part of $\frac{1}{13}$.