Transposable integer

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The digits of some specific integers permute or shift cyclically when they are multiplied by a number n. Examples are:

• 142857 × 3 = 428571 (shifts cyclically one place left)
• 142857 × 5 = 714285 (shifts cyclically one place right)
• 128205 × 4 = 512820 (shifts cyclically one place right)
• 076923 × 9 = 692307 (shifts cyclically two places left)

These specific integers, known as transposable integers, can be but are not always cyclic numbers. The characterization of such numbers can be done using repeating decimals (and thus the related fractions), or directly.