Unique-period primes in base 9, written in base 9.
5, 45, 81, 1552, 8801, 44444445, 888001, 88008801, 108778011, 4444444444444445, 888888000001, 888888888000000001, 44444444444444444444444444444445, 108780108778010878011, 8080808080808080808080808080808080808080808080808080808081
1
As in the base-10 case, these primes have a unique structure.
T. D. Noe, Plot of 39 terms
T. D. Noe, Table of 39 terms
Chris K. Caldwell, Unique prime
(Mma) nn = 100; t9 = Table[c = Cyclotomic[n, 9]; c/GCD[n, c], {n, 2, nn}]; p9 = Select[t9, PrimePowerQ]; p9 = Table[FactorInteger[i][[1, 1]], {i, p9}]; Table[FromDigits[IntegerDigits[i, 9]], {i, p9}]
Cf. A040017 (base-10 unique-period primes), A161509 (base 2).
Cf. S000025, S000032.
nonn,base
T. D. Noe, May 14 2014