Unique-period primes in base 4, written in base 4.
11, 13, 101, 31, 10001, 221, 3301, 100000001, 33003301, 330033003301, 3333000033330001, 10033323233000101, 33003300330033003300330033003300330033003301, 33333333333333330000000000000001, 333300003333000033330000333300003333000033330001
1
As in the base-10 case, these primes have a unique structure.
T. D. Noe, Plot of 32 terms
T. D. Noe, Table of 32 terms
Chris K. Caldwell, Unique prime
(Mma) nn = 100; t4 = Table[c = Cyclotomic[n, 4]; c/GCD[n, c], {n, 2, nn}]; p4 = Select[t4, PrimePowerQ]; p4 = Table[FactorInteger[i][[1, 1]], {i, p4}]; Table[FromDigits[IntegerDigits[i, 4]], {i, p4}]
Cf. A040017 (base-10 unique-period primes), A161509 (base 2), A064080.
Cf. S000020, S000027.
nonn,base
T. D. Noe, May 14 2014