Other Numeric Bases
Using the above technique, cyclic numbers can be found in other numeric bases. (Note that not all of these follow the second rule (all successive multiples being cyclic permutations) listed in the Special Cases section above)
In binary, the sequence of cyclic numbers begins:
- 01
- 0011
- 0001011101
- 000100111011
- 000011010111100101
In ternary:
- 0121
- 010212
- 0011202122110201
- 001102100221120122
- 0002210102011122200121202111
In octal:
- 25
- 1463
- 0564272135
- 0215173454106475626043236713
- 0115220717545336140465103476625570602324416373126743
In duodecimal:
- 2497
- 186A35
- 08579214B36429A7
In Base 24:
- 3A6LDH
- 248HAMKF6D
- 1L795CN3GEJB
- 19M45FCGNE2KJ8B7
Note that in ternary (b = 3), the case p = 2 yields 1 as a cyclic number. While single digits may be considered trivial cases, it may be useful for completeness of the theory to consider them only when they are generated in this way.
It can be shown that no cyclic numbers (other than trivial single digits) exist in any numeric base which is a perfect square; thus there are no cyclic numbers in hexadecimal.
Read more about this topic: Cyclic Number
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