The number (123…(b−1)) in base b has the property that when multiplied by any integer 1≤k≤b−1 which is coprime to b−1, its digits are permuted.
For example in base 10, 123456789
∗2 = 246913578
∗4 = 493827156
∗5 = 617283945
∗7 = 864197523
∗8 = 987654312
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