Unique-period primes in base 5, written in base 5.
3, 111, 23, 12, 1111111, 2223, 4041, 11111111111, 4401, 1111111111111, 131132, 44440001, 440044004401, 11111111111111111111111111111111111111111111111, 4444444400000001, 1000000100000010000001000000100000010000001, 444400004444000044440001
1
As in the base-10 case, these primes have a unique structure.
T. D. Noe, Plot of 53 terms
T. D. Noe, Table of 53 terms
Chris K. Caldwell, Unique prime
(Mma) nn = 100; t5 = Table[c = Cyclotomic[n, 5]; c/GCD[n, c], {n, 2, nn}]; p5 = Select[t5, PrimePowerQ]; p5 = Table[FactorInteger[i][[1, 1]], {i, p5}]; Table[FromDigits[IntegerDigits[i, 5]], {i, p5}]
Cf. A040017 (base-10 unique-period primes), A161509 (base 2), A064081.
Cf. S000021, S000028.
nonn,base
T. D. Noe, May 14 2014