Unique-period primes in base 7, written in base 7.
2, 25, 5, 11111, 61, 3334, 1111111111111, 666001, 600600660661, 660066006601, 106556011, 6060606060606061, 666666000001, 6060606060606060606061, 6666666600000001, 66666000006666600001, 666666666000000001, 6000060000660006600066600666006666066661
1
As in the base-10 case, these primes have a unique structure.
T. D. Noe, Plot of 48 terms
T. D. Noe, Table of 48 terms
Chris K. Caldwell, Unique prime
(Mma) nn = 100; t7 = Table[c = Cyclotomic[n, 7]; c/GCD[n, c], {n, 2, nn}]; p7 = Select[t7, PrimePowerQ]; p7 = Table[FactorInteger[i][[1, 1]], {i, p7}]; Table[FromDigits[IntegerDigits[i, 7]], {i, p7}]
Cf. A040017 (base-10 unique-period primes), A161509 (base 2), A064083.
Cf. S000023, S000030.
nonn,base
T. D. Noe, May 14 2014