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Reference.org
Transposable integer
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, the transposable integers are integers that <a href="/facts/Cyclic_permutation/UndoYWpl">permute</a> or <a href="/facts/Cyclic_shift/noSNJs87">shift</a> cyclically when they are multiplied by another integer n {\displaystyle n} . Examples are: </p> <ul><li>142857 × 3 = 428571 (shifts cyclically one place left)</li> <li>142857 × 5 = 714285 (shifts cyclically one place right)</li> <li>128205 × 4 = 512820 (shifts cyclically one place right)</li> <li>076923 × 9 = 692307 (shifts cyclically two places left)</li></ul> <p>These transposable integers can be but are not always <a href="/facts/Cyclic_number/cCQt6pAB">cyclic numbers</a>. The characterization of such numbers can be done using <a href="/facts/Repeating_decimals/yo5T4m2M">repeating decimals</a> (and thus the related fractions), or directly. </p>