Details
To qualify as a cyclic number, it is required that successive multiples be cyclic permutations. Thus, the number 076923 would not be considered a cyclic number, even though all cyclic permutations are multiples:
- 076923 × 1 = 076923
- 076923 × 3 = 230769
- 076923 × 4 = 307692
- 076923 × 9 = 692307
- 076923 × 10 = 769230
- 076923 × 12 = 923076
The following trivial cases are typically excluded:
- single digits, e.g.: 5
- repeated digits, e.g.: 555
- repeated cyclic numbers, e.g.: 142857142857
If leading zeros are not permitted on numerals, then 142857 is the only cyclic number in decimal. Allowing leading zeros, the sequence of cyclic numbers begins:
- 142857 (6 digits)
- 0588235294117647 (16 digits)
- 052631578947368421 (18 digits)
- 0434782608695652173913 (22 digits)
- 0344827586206896551724137931 (28 digits)
- 0212765957446808510638297872340425531914893617 (46 digits)
- 0169491525423728813559322033898305084745762711864406779661 (58 digits)
- 016393442622950819672131147540983606557377049180327868852459 (60 digits)
Read more about this topic: Cyclic Number
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