Numbers that are unique-period primes in bases 2 and 3.
5, 7, 13, 41, 73
1
Appears to be finite. Compare with S000017 and S000018.
Chris K. Caldwell, Unique prime
T. D. Noe, Plot of 5 terms
Examples:
1/5 repeats (1, 1, 0, 0) in base 2 and (1, 2, 1, 0) in base 3.
1/7 repeats (1, 0, 0) in base 2 and (1, 0, 2, 1, 2, 0) in base 3.
(Mma) nn = 500; t2 = Table[c = Cyclotomic[n, 2]; c/GCD[n, c], {n, 2, nn}]; t3 = Table[c = Cyclotomic[n, 3]; c/GCD[n, c], {n, 2, nn}]; Intersection[Select[t2, PrimePowerQ], Select[t3, PrimePowerQ]]
nonn,base
T. D. Noe, May 14 2014