A250288 Numbers n such that the duodecimal repunit (12^n - 1)/11 is a semiprime.

7, 13, 17, 37, 47, 73, 101, 131, 151, 167, 197, 241, 263

Offset: 1

Author

Eric Chen, Dec 18 2014

Keywords

• nonn
• more

Comments

First unknown term is 311.

If (12^n - 1)/11 is a semiprime, n must be prime or the square of a prime (A001248), but no n = prime squared is known which yields a semiprime value of (12^n - 1)/11. (Specifically, n must be the square of a prime in A004064, and must be at least 491401 = 701^2.)

No other known terms below 1000; the only other possible terms below 1000 are 449, 521, 571, 577, 613, 709, 751, 757, 769, 787, 853, 859, 887, 929, and 991.

Examples

			a(1) = 7 so 1111111 = 46E * 2X3E (written in base 12).
		

Links

• Samuel Wagstaff, The Cunningham Project

Crossrefs

Cf. A046413, A085724, A004064.

Programs

Mathematica

Select[Range[120], PrimeOmega[(12^# - 1)/11] == 2 &] (* Alonso del Arte, Dec 18 2014 *)