A115398 Numbers k such that both k^2+1 and 2^k + 1 are semiprimes.

3, 5, 11, 12, 19, 28, 61, 64, 79, 92, 101, 104, 199, 356, 596, 692, 1709, 3539, 3824

Offset: 1

Author

Zak Seidov, Mar 08 2006

Keywords

• nonn
• more

Comments

Intersection of A085722 and A092559.

Examples

			11 is a term because 11^2 + 1 = 122 = 2*61 (semiprime) and 2^11 + 1 = 2049 = 3*683 (semiprime).
		

Crossrefs

Cf. A085722, A092559.

Programs

Magma

IsSemiprime:=func; [n: n in [2..700] | IsSemiprime(n^2+1) and IsSemiprime(2^n+1)]; // Vincenzo Librandi, Oct 10 2013

Mathematica

Select[Range[700],PrimeOmega[#^2+1]==PrimeOmega[2^#+1]==2&] (* Harvey P. Dale, Apr 14 2019 *)

PARI

isok(n) = (bigomega(n^2+1) == 2) && (bigomega(2^n+1) == 2); \\ Michel Marcus, Oct 10 2013

Extensions

a(17)-a(19) from Robert Israel, Nov 27 2023