7,13,103,53,11,79,211,41,73,281,......

[Antreas P. Hatzipolakis]

Quoting JHC - RKG,_The Book of Numbers_, p. 162:

prime denominator p     3 7 11 13 17 19 23 29 31 37 41 43 47 53 59
number of circles       2 1  5  2  1  1  1  1  2 12  8  2  1  4  1
length of each circle   1 6  2  6 16 18 22 28 15  3  5 21 46 13 58

prime    61 67 71 73 79 83 89 97 101 103 107 109 113 127 131 137
number    1  2  2  9  6  2  2  1  25   3   2   1   1   3   1  17
length   60 33 35  8 13 41 44 96   4  34  53 108 112  42 130   8

prime   139 149 151 157 163 167 173 179 181 191 193 197 199 211
number    3   1   2   2   2   1   2   1   1   2   1   2   2   7
length   46 148  75  78  81 166  86 178 180  95 192  98  99  30

prime  223 227 229 233 239 241 251 257 263 269 271 277 281 283
number   1   2   1   1  34   8   5   1   1   1  54   4  10   2
length 222 113 228 232   7  30  50 256 262 268   5  69  28 141

Cycle structures for prime deniminators p, 3<=p<=283

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 From the above table we get the sequence of smallest primes whose
the number of circles is n:
(In other words: The sequence of smallest primes p such that the period of 1/p
is of length (p-1)/n.)

                 7,3,103,53,11,79,211,41,73,281,......

This sequence was not found in EIS:
<q>I am sorry, but the terms 7,3,103,53,11,79,211,41,73,281
do not match anything in the table.</q>

Note: The sequence of the number of the circles:
2,1,5,2,1,1,1,1,2,12,8,2,1,4,1,.... is A006556  in EIS


Antreas