Unique-period primes in base 6, written in base 6.
11, 111, 101, 1235, 51, 1111111, 10001, 555001, 500500550551, 5050505051, 55550001, 11111111111111111111111111111, 105445011, 1054500545011, 55555000005555500001, 505050505050505050505050505051
1
The next term has 71 ones. As in the base-10 case, these primes have a unique structure.
T. D. Noe, Plot of 43 terms
T. D. Noe, Table of 43 terms
Chris K. Caldwell, Unique prime
(Mma) nn = 100; t6 = Table[c = Cyclotomic[n, 6]; c/GCD[n, c], {n, 2, nn}]; p6 = Select[t6, PrimePowerQ]; p6 = Table[FactorInteger[i][[1, 1]], {i, p6}]; Table[FromDigits[IntegerDigits[i, 6]], {i, p6}]
Cf. A040017 (base-10 unique-period primes), A161509 (base 2), A064082.
Cf. S000022, S000029.
nonn,base
T. D. Noe, May 14 2014