Unique-period primes in base 3, written in base 3.
2, 111, 12, 102, 21, 1111111, 1112, 1001001, 2021, 2201, 1111111111111, 202021, 20020221, 1121202, 200200220221, 22220001, 202020202021, 1111111111111112, 20020020020220220221, 222222000001, 2222000022220001, 2020202020202020202021
1
As in the base-10 case, these primes have a unique structure.
T. D. Noe, Plot of 66 terms
T. D. Noe, Table of 66 terms
Chris K. Caldwell, Unique prime
(Mma) nn = 100; t3 = Table[c = Cyclotomic[n, 3]; c/GCD[n, c], {n, 2, nn}]; p3 = Select[t3, PrimePowerQ]; p3 = Table[FactorInteger[i][[1, 1]], {i, p3}]; Table[FromDigits[IntegerDigits[i, 3]], {i, p3}]
Cf. A040017 (base-10 unique-period primes), A161509 (base 2), A064079.
Cf. S000019, S000026.
nonn,base
T. D. Noe, May 14 2014