A309358 Numbers k such that 10^k + 1 is a semiprime.

4, 5, 6, 7, 8, 19, 31, 53, 67, 293, 586, 641, 922, 2137, 3011

Offset: 1

Author

Hugo Pfoertner, Jul 29 2019

Keywords

• nonn
• more
• hard

Comments

a(16) > 12000.

10^k + 1 is composite unless k is a power of 2, and it can be conjectured that it is composite for all k > 2, cf. A038371 and A185121. - M. F. Hasler, Jul 30 2019

Suppose k is odd. Then k is a term if and only if (10^k+1)/11 is prime. - Chai Wah Wu, Jul 31 2019

Examples

			a(1) = 4 because 10^4 + 1 = 10001 = 73*137.
		

Crossrefs

Cf. A003021, A038371, A046413, A057934, A062397, A092559.

Odd terms in sequence: A001562.

Programs

Magma

IsSemiprime:=func; [n: n in [2..200] | IsSemiprime(s) where s is 10^n+1]; // Vincenzo Librandi, Jul 31 2019

Mathematica

Select[Range[200], Plus@@Last/@FactorInteger[10^# + 1] == 2 &] (* Vincenzo Librandi, Jul 31 2019 *)